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  • Statistics In Transition

 

Article | 13-December-2019

LINEAR CHOLESKY DECOMPOSITION OF COVARIANCE MATRICES IN MIXED MODELS WITH CORRELATED RANDOM EFFECTS

Modelling the covariance matrix in linear mixed models provides an additional advantage in making inference about subject-specific effects, particularly in the analysis of repeated measurement data, where time-ordering of the responses induces significant correlation. Some difficulties encountered in these modelling procedures include high dimensionality and statistical interpretability of parameters, positive definiteness constraint and violation of model assumptions. One key assumption in linear

Anasu Rabe, D. K. Shangodoyin, K. Thaga

Statistics in Transition New Series, Volume 20 , ISSUE 4, 59–70

Research Article | 24-August-2017

A MULTIDIMENSIONAL AND DYNAMISED CLASSIFICATION OF POLISH PROVINCES BASED ON SELECTED FEATURES OF HIGHER EDUCATION IN 2002–2013

of features relating to higher education. To investigate the changes in higher education in the period of economic and social transformation, observations were made of fundamental characteristics of higher education in the years 2002–2013. The applied procedure uses new statistical methods applicable to a space of doubly multivariate data. The covariance matrix used to construct principal components is given the structure of a Kronecker product. The results led to the identification of six groups

Wojciech Łukaszonek

Statistics in Transition New Series, Volume 18 , ISSUE 2, 271–290

Research Article | 27-May-2018

CANONICAL CORRELATION ANALYSIS IN THE CASE OF MULTIVARIATE REPEATED MEASURES DATA

In this paper, we present, in the real example, canonical variables applicable in the case of multivariate repeated measures data under the following assumptions: (1) multivariate normality for the vector of observations and (2) Kronecker product structure of the positive definite covariance matrix. These variables are especially useful when the number of observations is not large enough to estimate the covariance matrix, and thus the traditional canonical variables fail. Computational schemes

Mirosław Krzyśko, Wojciech Łukaszonek, Waldemar Wołyński

Statistics in Transition New Series, Volume 19 , ISSUE 1, 75–85

Research Article | 13-December-2018

DEALING WITH HETEROSKEDASTICITY WITHIN  THE MODELING OF THE QUALITY OF LIFE  OF OLDER PEOPLE

Using the estimation method of ordinary least squares leads to unreliable results in the case of heteroskedastic linear regression model. Other estimation methods are described, including weighted least squares, division of the sample and heteroskedasticity-consistent covariance matrix estimators, all of which can give estimators with better properties than ordinary least squares. The methods are presented giving the example of modelling quality of life of older people, based on a data set from

Katarzyna Jabłońska

Statistics in Transition New Series, Volume 19 , ISSUE 3, 423–452

Article | 22-July-2019

TESTING HYPOTHESES ABOUT STRUCTURE OF PARAMETERS IN MODELS WITH BLOCK COMPOUND SYMMETRIC COVARIANCE STRUCTURE

In this article we deal with testing the hypotheses of the so-called structured mean vector and the structure of a covariance matrix. For testing the above mentioned hypotheses Jordan algebra properties are used and tests based on best quadratic unbiased estimators (BQUE) are constructed. For convenience coordinate-free approach (see Kruskal (1968) and Drygas (1970)) is used as a tool for characterization of best unbiased estimators and testing hypotheses. To obtain the test for mean vector

Roman Zmyslony, Arkadiusz Kozioł

Statistics in Transition New Series, Volume 20 , ISSUE 2, 139–153

Article | 15-September-2020

An evaluation of design-based properties of different composite estimators

For the last several decades, the US Census Bureau has been applying AK composite estimation method for estimating monthly levels and month-to-month changes in unemployment using data from the Current Population Survey (CPS), which uses a rotating panel design. For each rotation group, survey-weighted totals, known as monthin-sample estimates, are derived each month to estimate population totals. Denoting the vector of month-in-sample estimates by Y and the design-based variance-covariance

Daniel Bonnéry, Yang Cheng, Partha Lahiri

Statistics in Transition New Series, Volume 21 , ISSUE 4, 166–190

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