| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
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| 8. |
- Curic, Vladimir, et al.
(författare)
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Salience-Based Parabolic Structuring Functions
- 2013
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Ingår i: Mathematical Morphology and Its Applications to Signal and Image Processing. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783642382932 ; 7883, s. 183-194
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Konferensbidrag (refereegranskat)abstract
- It has been shown that the use of the salience map based on the salience distance transform can be useful for the construction of spatially adaptive structuring elements. In this paper, we propose salience-based parabolic structuring functions that are defined for a fixed, predefined spatial support, and have low computational complexity. In addition, we discuss how to properly define adjunct morphological operators using the new spatially adaptive structuring functions. It is also possible to obtain flat adaptive structuring elements by thresholding the salience-based parabolic structuring functions.
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| 9. |
- Galindo-Prieto, Beatriz, et al.
(författare)
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A new approach for variable influence on projection (VIP) in O2PLS models
- 2017
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Ingår i: Chemometrics and Intelligent Laboratory Systems. - : Elsevier. - 0169-7439 .- 1873-3239. ; 160, s. 110-124
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Tidskriftsartikel (refereegranskat)abstract
- A novel variable influence on projection approach for O2PLS® models, named VIPO2PLS, is presented in this paper. VIPO2PLS is a model-based method for judging the importance of variables. Its cornerstone is the 2-way formalism of the O2PLS models; i.e. the use of both predictive and orthogonal normalized loadings of the two modelled data matrices, and also a new weighting system based on the sum of squares of both data blocks (X, Y). The VIPO2PLS algorithm has been tested in one synthetic data set and two real cases, and the outcomes have been compared to the PLS-VIP, VIPOPLS, and i-PLS methods. The purpose is to achieve a sharper and enhanced model interpretation of O2PLS models by using the new VIPO2PLS method for assessing the importance of both X- and Y- variables.
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| 10. |
- Malmberg, Filip, et al.
(författare)
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An efficient algorithm for exact evaluation of stochastic watersheds
- 2014
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Ingår i: Pattern Recognition Letters. - : Elsevier BV. - 0167-8655 .- 1872-7344. ; 47, s. 80-84
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Tidskriftsartikel (refereegranskat)abstract
- The stochastic watershed is a method for unsupervised image segmentation proposed by Angulo and Jeulin (2007). The method first computes a probability density function (PDF), assigning to each piece of contour in the image the probability to appear as a segmentation boundary in seeded watershed segmentation with randomly selected seeds. Contours that appear with high probability are assumed to be more important. This PDF is then post-processed to obtain a final segmentation. The main computational hurdle with the stochastic watershed method is the calculation of the PDF. In the original publication by Angulo and Jeulin, the PDF was estimated by Monte Carlo simulation, i.e., repeatedly selecting random markers and performing seeded watershed segmentation. Meyer and Stawiaski (2010) showed that the PDF can be calculated exactly, without performing any Monte Carlo simulations, but do not provide any implementation details. In a naive implementation, the computational cost of their method is too high to make it useful in practice. Here, we extend the work of Meyer and Stawiaski by presenting an efficient (quasi-linear) algorithm for exact computation of the PDF. We demonstrate that in practice, the proposed method is faster than any previously reported method by more than two orders of magnitude. The algorithm is formulated for general undirected graphs, and thus trivially generalizes to images with any number of dimensions.
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