Singull, Martin
Overview
Works:  28 works in 34 publications in 2 languages and 200 library holdings 

Roles:  Editor, htt, Author, Thesis advisor, Other 
Classifications:  QA278, 519.5 
Publication Timeline
.
Most widely held works by
Martin Singull
Recent Developments in Multivariate and Random Matrix Analysis : Festschrift in Honour of Dietrich von Rosen(
)
6 editions published between 2020 and 2021 in English and held by 171 WorldCat member libraries worldwide
This volume is a tribute to Professor Dietrich von Rosen on the occasion of his 65th birthday. It contains a collection of twenty original papers. The contents of the papers evolve around multivariate analysis and random matrices with topics such as highdimensional analysis, goodnessoffit measures, variable selection and information criteria, inference of covariance structures, the Wishart distribution and growth curve models.
6 editions published between 2020 and 2021 in English and held by 171 WorldCat member libraries worldwide
This volume is a tribute to Professor Dietrich von Rosen on the occasion of his 65th birthday. It contains a collection of twenty original papers. The contents of the papers evolve around multivariate analysis and random matrices with topics such as highdimensional analysis, goodnessoffit measures, variable selection and information criteria, inference of covariance structures, the Wishart distribution and growth curve models.
Smallarea estimation with missing data using a multivariate linear random effects model by
Innocent Ngaruye(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
Studies in estimation of patterned covariance matrices by
Martin Ohlson(
Book
)
2 editions published in 2009 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2009 in English and held by 2 WorldCat member libraries worldwide
Testing spatial independence using a separable covariance matrix by
Martin Ohlson(
Book
)
1 edition published in 2007 in Swedish and held by 1 WorldCat member library worldwide
1 edition published in 2007 in Swedish and held by 1 WorldCat member library worldwide
Large deviations of condition numbers of random matrices by
Denise Uwamariya(
)
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
Evaluation Report of the Eastern Africa Universities Mathematics Programme (EAUMP) by
Martin Singull(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
The Eastern Africa Universities Mathematics Programme (EAUMP) was launched in 2002 by the International Science Programme (ISP) with support fromthe Swedish International Development Cooperation Agency (Sida) in collaboration with the Departments of Mathematics at University of Nairobi, Kenya; University of Dar es Salaam, Tanzania; and Makerere University, Uganda. The Mathematics Departments of the University of Rwanda and the University of Zambia joined the EAUMP network in the late 2000s. The main activities of the network have consisted of capacity building via training PhD and MSc students; organizing mathematics Conferences and Summer schools; network exchange visits and coordinator meetings; research visits for postdocs to Sweden and elsewhere; as well as support for building up equipment and for research expenses. The total ISP support to EAUMP for the period 20022016 was 29,259,902 SEK or (at the current exchange rates) EUR 2.99M or USD 3.12M. It is the view of the Evaluation Team that the EAUMP network has played an absolutely essential and transformative role, at a reasonable and proportionate cost, in building mathematics research and teaching capacity throughout the Eastern African region, introducing new areas of mathematics and strengthening existing ones. There are signs of consolidating and emerging research groups, regular activities becoming embedded and finding additional support, as well as new types of activity. The continuing support, in a suitable form and shape, and taking into account the recommendations below, of mathematics, the most fundamental of enabling sciences, in the East African region is a worthwhile endeavour fully in accordance with the aims and objectives of ISP and its main funder Sida
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
The Eastern Africa Universities Mathematics Programme (EAUMP) was launched in 2002 by the International Science Programme (ISP) with support fromthe Swedish International Development Cooperation Agency (Sida) in collaboration with the Departments of Mathematics at University of Nairobi, Kenya; University of Dar es Salaam, Tanzania; and Makerere University, Uganda. The Mathematics Departments of the University of Rwanda and the University of Zambia joined the EAUMP network in the late 2000s. The main activities of the network have consisted of capacity building via training PhD and MSc students; organizing mathematics Conferences and Summer schools; network exchange visits and coordinator meetings; research visits for postdocs to Sweden and elsewhere; as well as support for building up equipment and for research expenses. The total ISP support to EAUMP for the period 20022016 was 29,259,902 SEK or (at the current exchange rates) EUR 2.99M or USD 3.12M. It is the view of the Evaluation Team that the EAUMP network has played an absolutely essential and transformative role, at a reasonable and proportionate cost, in building mathematics research and teaching capacity throughout the Eastern African region, introducing new areas of mathematics and strengthening existing ones. There are signs of consolidating and emerging research groups, regular activities becoming embedded and finding additional support, as well as new types of activity. The continuing support, in a suitable form and shape, and taking into account the recommendations below, of mathematics, the most fundamental of enabling sciences, in the East African region is a worthwhile endeavour fully in accordance with the aims and objectives of ISP and its main funder Sida
Misclassification Probabilities through Edgeworthtype Expansion for the Distribution of the Maximum Likelihood based Discriminant
Function by
Emelyne Umunoza Gasana(
)
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
This thesis covers misclassification probabilities via an Edgeworthtype expansion of the maximum likelihood based discriminant function. When deriving misclassification errors, first the expectation and variance in the population are assumed to be known where the variance is the same across populations and thereafter we consider the case where those parameters are unknown. Cumulants of the discriminant function for discriminating between two multivariate normal populations are derived. Approximate probabilities of the misclassification errors are established via an Edgeworthtype expansion using a standard normal distribution
1 edition published in 2021 in English and held by 1 WorldCat member library worldwide
This thesis covers misclassification probabilities via an Edgeworthtype expansion of the maximum likelihood based discriminant function. When deriving misclassification errors, first the expectation and variance in the population are assumed to be known where the variance is the same across populations and thereafter we consider the case where those parameters are unknown. Cumulants of the discriminant function for discriminating between two multivariate normal populations are derived. Approximate probabilities of the misclassification errors are established via an Edgeworthtype expansion using a standard normal distribution
On the Distribution of Matrix Quadratic Forms by
Martin Ohlson(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
A characterization of the distribution of the multivariate quadratic form given by XAX2, where X is a p×n normally distributed matrix and A is an n×n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentralWishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
A characterization of the distribution of the multivariate quadratic form given by XAX2, where X is a p×n normally distributed matrix and A is an n×n symmetric real matrix, is presented. We show that the distribution of the quadratic form is the same as the distribution of a weighted sum of noncentralWishart distributed matrices. This is applied to derive the distribution of the sample covariance between the rows of X when the expectation is the same for every column and is estimated with the regular mean
Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured CovarianceMatrices by
Martin Ohlson(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Estimation of parameters in the classical Growth Curve model when the covariance matrix has some specific linear structure is considered. In our examples maximum likelihood estimators can not be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple noniterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Estimation of parameters in the classical Growth Curve model when the covariance matrix has some specific linear structure is considered. In our examples maximum likelihood estimators can not be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple noniterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix
International Conference on Trends and Perspectives in Linear Statistical Inference and 21st International Workshop on Matrices
and Statistics, July 1620, 2012 Będlewo, Poland : book of abstracts by International Conference on Trends and Perspectives in Linear Statistical Inference(
Book
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
A note on mean testing for high dimensional multivariate data under nonnormality by M. Rauf Ahmad(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p ₂!, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chisquare distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the wellknown Box's approximation, under highdimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p ₂!, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chisquare distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the wellknown Box's approximation, under highdimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p
Contributions to linear discriminant analysis with applications to growth curves by
Edward Kanuti Ngailo(
Book
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
Den här avhandlingen studerar diskriminantanalys, klassificering av tillväxtkurvor och portföljteori. Diskriminantanalys och klassificering är flerdimensionella tekniker som används för att separera olika mängder av objekt och för att tilldela nya objekt till redan definierade grupper (så kallade klasser). En klassisk metod är att använda Fishers linjära diskriminantfunktion och när alla parametrar är kända så kan man enkelt beräkna sannolikheterna för felklassificering. Tyvärr är så sällan fallet, utan parametrarna måste skattas från data, och då blir Fishers linjära diskriminantfunktion en funktion av en Wishartmatris och multivariat normalfördelade vektorer. I den här avhandlingen studerar vi hur man kan approximativt beräkna sannolikheten för felklassificering under antagande att dimensionen på parameterrummet ökar tillsammans med antalet observationer genom att använda en särskild stokastisk representation av diskriminantfunktionen. Upprepade mätningar över tiden på samma individ eller objekt går att modellera med så kallade tillväxtkurvor. Vid klassificering av tillväxtkurvor, eller rättare sagt av upprepade mätningar för en ny individ, bör man ta tillvara på både den spatiala och temporala informationen som finns hos dessa observationer. Vi vidareutvecklar Fishers linjära diskriminantfunktion att passa för upprepade mätningar och beräknar asymptotiska sannolikheter för felklassificering. Till sist kan man notera att snarlika funktioner av Wishartmatriser och multivariat normalfördelade vektorer dyker upp när man vill beräkna de optimala vikterna i portföljteori. Genom en stokastisk representation studerar vi egenskaperna hos portföljvikterna och gör dessutom en simuleringsstudie för att förstå vad som händer när antagandet om normalfördelning inte är uppfyllt
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
Den här avhandlingen studerar diskriminantanalys, klassificering av tillväxtkurvor och portföljteori. Diskriminantanalys och klassificering är flerdimensionella tekniker som används för att separera olika mängder av objekt och för att tilldela nya objekt till redan definierade grupper (så kallade klasser). En klassisk metod är att använda Fishers linjära diskriminantfunktion och när alla parametrar är kända så kan man enkelt beräkna sannolikheterna för felklassificering. Tyvärr är så sällan fallet, utan parametrarna måste skattas från data, och då blir Fishers linjära diskriminantfunktion en funktion av en Wishartmatris och multivariat normalfördelade vektorer. I den här avhandlingen studerar vi hur man kan approximativt beräkna sannolikheten för felklassificering under antagande att dimensionen på parameterrummet ökar tillsammans med antalet observationer genom att använda en särskild stokastisk representation av diskriminantfunktionen. Upprepade mätningar över tiden på samma individ eller objekt går att modellera med så kallade tillväxtkurvor. Vid klassificering av tillväxtkurvor, eller rättare sagt av upprepade mätningar för en ny individ, bör man ta tillvara på både den spatiala och temporala informationen som finns hos dessa observationer. Vi vidareutvecklar Fishers linjära diskriminantfunktion att passa för upprepade mätningar och beräknar asymptotiska sannolikheter för felklassificering. Till sist kan man notera att snarlika funktioner av Wishartmatriser och multivariat normalfördelade vektorer dyker upp när man vill beräkna de optimala vikterna i portföljteori. Genom en stokastisk representation studerar vi egenskaperna hos portföljvikterna och gör dessutom en simuleringsstudie för att förstå vad som händer när antagandet om normalfördelning inte är uppfyllt
Small Area Estimation under a Multivariate Linear Model for Repeated measures Data by
Innocent Ngaruye(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
In this article, Small Area Estimation under a Multivariate Linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
In this article, Small Area Estimation under a Multivariate Linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study
Asset Liability Management for Tanzania Pension Funds by
Andongwisye John Mwakisisile(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
This thesis presents a longterm asset liability management for Tanzania pension funds. As an application, the largest pension fund in Tanzania is considered. This is a payasyougo pension fund where the contributions are used to pay current benefits. The Pension plan analyzed is a final salary defined benefit. Two kinds of pension benefit are considered, a commuted (at retirement) and a monthly (old age) pension. A decision factor in the analysis is the increased life expectancy of the members of the pension fund. The presentation is divided into two parts. First is a longterm projection of the fund using a fixed and relatively low return on asset value. Basing on the number of members in 2015, a 50 years projection of members and retirees is done. The corresponding amount of contributions, asset values, benefit payouts, and liabilities are also projected. The evaluation of some possible reforms of the fund is done. Then, the growth of asset values using different asset returns is studied. The projection shows that the fund will not be fully sustainable in a long future due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some reforms of the fund shows that they cannot guarantee a longterm sustainability. Higher returns on asset value will improve the asset to liability ratio, but contributions are still insufficient to cover benefit payouts. Second is a management based on stochastic programming. This approach allocates investment in assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001 includes some features from Tanzania pension system. In contrast with most asset liability management models for pension funds by stochastic programming, liabilities are modeled by number of years of life expectancy. Scenario trees are generated by using Monte Carlo simulation. Two models according to different investment guidelines are built. First is using the existing investment guidelines and ii second is using modified guidelines which are practical and suitable for modeling. Numerical results suggest that, in order to improve a longterm sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target levels (funding ratios) to characterize the pension funds' solvency situation. These reforms will improve the sustainability of the system
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
This thesis presents a longterm asset liability management for Tanzania pension funds. As an application, the largest pension fund in Tanzania is considered. This is a payasyougo pension fund where the contributions are used to pay current benefits. The Pension plan analyzed is a final salary defined benefit. Two kinds of pension benefit are considered, a commuted (at retirement) and a monthly (old age) pension. A decision factor in the analysis is the increased life expectancy of the members of the pension fund. The presentation is divided into two parts. First is a longterm projection of the fund using a fixed and relatively low return on asset value. Basing on the number of members in 2015, a 50 years projection of members and retirees is done. The corresponding amount of contributions, asset values, benefit payouts, and liabilities are also projected. The evaluation of some possible reforms of the fund is done. Then, the growth of asset values using different asset returns is studied. The projection shows that the fund will not be fully sustainable in a long future due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some reforms of the fund shows that they cannot guarantee a longterm sustainability. Higher returns on asset value will improve the asset to liability ratio, but contributions are still insufficient to cover benefit payouts. Second is a management based on stochastic programming. This approach allocates investment in assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001 includes some features from Tanzania pension system. In contrast with most asset liability management models for pension funds by stochastic programming, liabilities are modeled by number of years of life expectancy. Scenario trees are generated by using Monte Carlo simulation. Two models according to different investment guidelines are built. First is using the existing investment guidelines and ii second is using modified guidelines which are practical and suitable for modeling. Numerical results suggest that, in order to improve a longterm sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target levels (funding ratios) to characterize the pension funds' solvency situation. These reforms will improve the sustainability of the system
On distributions of Matrix Quadratic forms by
Martin Ohlson(
Book
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
MeanSquared errors of small area estimators under a multivariate linear model for repeated measures data by
Innocent Ngaruye(
)
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the meansquared errors (MSE) for the predicted small area means as a measure of precision. At the first stage, we derive the MSE when the covariance matrices are known. At the second stage, a method based on parametric bootstrap is proposed for bias correction and for prediction error that reflects the uncertainty when the unknown covariance is replaced by its suitable estimator
1 edition published in 2019 in English and held by 1 WorldCat member library worldwide
In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the meansquared errors (MSE) for the predicted small area means as a measure of precision. At the first stage, we derive the MSE when the covariance matrices are known. At the second stage, a method based on parametric bootstrap is proposed for bias correction and for prediction error that reflects the uncertainty when the unknown covariance is replaced by its suitable estimator
The Likelihood Ratio Statistic for testing Spatial Independence using a Separable Covariance Matrix by
Martin Ohlson(
Book
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
More on the Kronecker Structured Covariance Matrix by
Martin Ohlson(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
In this paper, the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly focused is the estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The suggested estimation generalizes the procedure proposed by Srivastava et al. (2008) for a separable covariance matrix. The restrictions imposed by separability and double separability are also discussed
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
In this paper, the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly focused is the estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The suggested estimation generalizes the procedure proposed by Srivastava et al. (2008) for a separable covariance matrix. The restrictions imposed by separability and double separability are also discussed
Explicit Estimators under mDependence for a Multivariate Normal Distribution by
Martin Ohlson(
)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
The problemof estimating parameters of amultivariate normal pdimensional random vector is considered for a banded covariance structure reflecting mdependence. A simple noniterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
The problemof estimating parameters of amultivariate normal pdimensional random vector is considered for a banded covariance structure reflecting mdependence. A simple noniterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m
Testing sphericity and intraclass covariance structures under a Growth Curve model in high dimension by
M. S Srivastava(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
In this article, we consider the problem of testing (a) sphericity and (b) intraclass covariance structure under a growth curve model. The maximum likelihood estimator (MLE) for the mean in a growth curve model is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N . The MLE for the covariance matrix is based on the MLE for the mean, which can be very poor for p close to N . For both structures (a) and (b), we modify the MLE for the mean to an unweighted estimator and based on this estimator we propose a new estimator for the covariance matrix. This new estimator leads to new tests for (a) and (b). We also propose two other tests for each structure, which are just based on the sample covariance matrix. To compare the performance of all four tests we compute for each structure (a) and (b) the attained significance level and the empirical power. We show that one of the tests based on the sample covariance matrix is better than the likelihood ratio test based on the MLE
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
In this article, we consider the problem of testing (a) sphericity and (b) intraclass covariance structure under a growth curve model. The maximum likelihood estimator (MLE) for the mean in a growth curve model is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N . The MLE for the covariance matrix is based on the MLE for the mean, which can be very poor for p close to N . For both structures (a) and (b), we modify the MLE for the mean to an unweighted estimator and based on this estimator we propose a new estimator for the covariance matrix. This new estimator leads to new tests for (a) and (b). We also propose two other tests for each structure, which are just based on the sample covariance matrix. To compare the performance of all four tests we compute for each structure (a) and (b) the attained significance level and the empirical power. We show that one of the tests based on the sample covariance matrix is better than the likelihood ratio test based on the MLE
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Related Identities
 Holgersson, Thomas Editor
 Rosen, Dietrich von Other Thesis advisor
 Linköpings universitet Matematiska institutionen Publisher
 Linköpings universitet Tekniska högskolan Publisher
 Von Rosen, Dietrich
 Ngaruye, Innocent Author
 Ahmad, M. Rauf Author
 Ngailo, Edward 1982 Author
 Koski, Timo 1952
 Yang, Xiangfeng 1983 Thesis advisor
Associated Subjects