| 1. |
- Lundengård, Karl, 1987-
(författare)
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Generalized Vandermonde matrices and determinants in electromagnetic compatibility
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.
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| 2. |
- Ohlson, Martin, et al.
(författare)
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Explicit Estimators of Parameters in the Growth Curve Model with Linearly Structured CovarianceMatrices
- 2010
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Ingår i: Journal of Multivariate Analysis. - : Elsevier BV. - 0047-259X .- 1095-7243. ; 101:5, s. 1284-1295
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Tidskriftsartikel (refereegranskat)abstract
- 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 non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix.
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| 3. |
- Pielaszkiewicz, Jolanta Maria, et al.
(författare)
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On n/p-Asymptotic Distribution Of Vector Of Weighted Traces Of Powers Of Wishart Matrice
- 2018
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Ingår i: The Electronic Journal of Linear Algebra. - Pensacola, FL, United States : International Linear Algebra Society. - 1537-9582 .- 1081-3810. ; 33, s. 24-40
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Tidskriftsartikel (refereegranskat)abstract
- The joint distribution of standardized traces of 1/n XX' and of (1/n XX')(2), where the matrix X : p x n follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition n/p ->(n,p ->infinity) c> 0. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of n and p.
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| 4. |
- Pielaszkiewicz, Jolanta Maria, 1985-, et al.
(författare)
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Cumulant-moment relation in free probability theory
- 2014
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Ingår i: Acta et Commentationes Universitatis Tartuensis de Mathematica. - : Tartu University Press. - 1406-2283 .- 2228-4699. ; 18:2, s. 265-278
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Tidskriftsartikel (refereegranskat)abstract
- The goal of this paper is to present and prove a cumulant-moment recurrent relation formula in free probability theory. It is convenient tool to determine underlying compactly supported distribution function. The existing recurrent relations between these objects require the combinatorial understanding of the idea of non-crossing partitions, which has been considered by Speicher and Nica. Furthermore, some formulations are given with additional use of the Möbius function. The recursive result derived in this paper does not require introducing any of those concepts. Similarly like the non-recursive formulation of Mottelson our formula demands only summing over partitions of the set. The proof of non-recurrent result is given with use of Lagrange inversion formula, while in our proof the calculations of the Stieltjes transform of the underlying measure are essential.
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| 5. |
- Ohlson, Martin, et al.
(författare)
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Explicit Estimators under m-Dependence for a Multivariate Normal Distribution
- 2011
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Ingår i: Annals of the Institute of Statistical Mathematics. - : Springer. - 0020-3157 .- 1572-9052. ; 63:1, s. 29-42
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Tidskriftsartikel (refereegranskat)abstract
- The problemof estimating parameters of amultivariate normal p-dimensional random vector is considered for a banded covariance structure reflecting mdependence. A simple non-iterative 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.
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| 6. |
- Ohlson, Martin, 1977-, et al.
(författare)
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More on the Kronecker Structured Covariance Matrix
- 2012
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 41:13-14, s. 2512-2523
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Ohlson, Martin, 1977-, et al.
(författare)
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The Multilinear Normal Distribution: Introduction and Some Basic Properties
- 2013
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Ingår i: Journal of Multivariate Analysis. - Maryland Heights, MO, United States : Academic Press. - 0047-259X .- 1095-7243. ; 113:S1, s. 37-47
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented.The estimation of parameters using a flip-flop algorithm is also briefly discussed.
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| 8. |
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| 9. |
- Ahmad, M. Rauf, et al.
(författare)
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Tests for high-dimensional covariance matrices using the theory of U-statistics
- 2015
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Ingår i: Journal of Statistical Computation and Simulation. - : Informa UK Limited. - 0094-9655 .- 1563-5163. ; 85:13, s. 2619-2631
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Tidskriftsartikel (refereegranskat)abstract
- Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.
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| 10. |
- Nzabanita, Joseph, et al.
(författare)
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Bilinear regression model with Kronecker and linear structures for the covariance matrix
- 2015
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Ingår i: Afrika Statistika. - : Statistics and Probability African Society (SPAS). - 2316-090X. ; 10:2, s. 827-837
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the bilinear regression model based on normally distributed random matrix is studied. For these models, the dispersion matrix has the so called Kronecker product structure and they can be used for example to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations in a flip-flop relation are established and the consistency of estimators is studied.
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