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Changepoint estimation for dependent and non-stationary panels

Michal Pešta, Barbora Peštová, Matúš Maciak (2020)

Applications of Mathematics

The changepoint estimation problem of a common change in panel means for a very general panel data structure is considered. The observations within each panel are allowed to be generally dependent and non-stationary. Simultaneously, the panels are weakly dependent and non-stationary among each other. The follow up period can be extremely short and the changepoint magnitudes may differ across the panels accounting also for a specific situation that some magnitudes are equal to zero (thus, no jump...

Classifiers for doubly multivariate data

Mirosław Krzyśko, Michał Skorzybut, Waldemar Wołyński (2011)

Discussiones Mathematicae Probability and Statistics

This paper proposes new classifiers under the assumption of multivariate normality for multivariate repeated measures data (doubly multivariate data) with Kronecker product covariance structures. These classifiers are especially useful when the number of observations is not large enough to estimate the covariance matrices, and thus the traditional classifiers fail. The quality of these new classifiers is examined on some real data. Computational schemes for maximum likelihood estimates of required...

Colinearité et Instabilité Numérique dans le Modèle Linéaire

Thierry Foucart (2010)

RAIRO - Operations Research

In this paper we give the expression of the multiple correlation coefficient in a linear model according to the coefficients of correlation. This expression makes it possible to analyze from a numerical point of view the instability of estimates in the case of collinear explanatory variables in the linear model or in the autoregressive model. This numerical approach, that we show on two examples, thus supplements the usual approach of the quasi colinearity, founded on the statistical properties...

Combining multivariate estimators of the mean vector

Iwona Janicka (2005)

Discussiones Mathematicae Probability and Statistics

Meta-analysis is a standard statistical method used to combine the conclusions of individual studies that are related and the results of single study alone can not answered to deal with issues. The data are summarized by one or more outcome measure estimates along with their standard errors. The multivariate model and the variations between studies are not considered in most articles. Here we discuss multivariate effects models: a multivariate fixed effects model and a multivariate random effects...

Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models

Aníbal Areia, Francisco Carvalho, João T. Mexia (2015)

Open Mathematics

We will discuss orthogonal models and error orthogonal models and their algebraic structure, using as background, commutative Jordan algebras. The role of perfect families of symmetric matrices will be emphasized, since they will play an important part in the construction of the estimators for the relevant parameters. Perfect families of symmetric matrices form a basis for the commutative Jordan algebra they generate. When normality is assumed, these perfect families of symmetric matrices will ensure...

Concomitants and linear estimators in an i-dimensional extremal model.

M. Ivette Gomes (1985)

Trabajos de Estadística e Investigación Operativa

We consider here a multivariate sample Xj = (X1.j > ... > Xi.j), 1 ≤ j ≤ n, where the Xj, 1 ≤ j ≤ n, are independent i-dimensional extremal vectors with suitable unknown location and scale parameters λ and δ respectively. Being interested in linear estimation of these parameters, we consider the multivariate sample Zj, 1 ≤ j ≤ n, of the order statistic of largest values and their concomitants, and the best linear unbiased estimators of λ and δ based on such multivariate sample. Computational...

Consistency of the least weighted squares under heteroscedasticity

Jan Ámos Víšek (2011)

Kybernetika

A robust version of the Ordinary Least Squares accommodating the idea of weighting the order statistics of the squared residuals (rather than directly the squares of residuals) is recalled and its properties are studied. The existence of solution of the corresponding extremal problem and the consistency under heteroscedasticity is proved.

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