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Test for Independence of the Variables with Missing Elements in One and the Same Column of the Empirical Correlation Matrix

Veleva, Evelina (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 62H15, 62H12.We consider variables with joint multivariate normal distribution and suppose that the sample correlation matrix has missing elements, located in one and the same column. Under these assumptions we derive the maximum likelihood ratio test for independence of the variables. We obtain also the maximum likelihood estimations for the missing values.

Test of linear hypothesis in multivariate models

Lubomír Kubáček (2007)

Kybernetika

In regular multivariate regression model a test of linear hypothesis is dependent on a structure and a knowledge of the covariance matrix. Several tests procedures are given for the cases that the covariance matrix is either totally unknown, or partially unknown (variance components), or totally known.

Testing hypotheses in universal models

Eva Fišerová (2006)

Discussiones Mathematicae Probability and Statistics

A linear regression model, when a design matrix has not full column rank and a covariance matrix is singular, is considered. The problem of testing hypotheses on mean value parameters is studied. Conditions when a hypothesis can be tested or when need not be tested are given. Explicit forms of test statistics based on residual sums of squares are presented.

Tests de la razón de verosimilitud para medias de poblaciones normales, sujetas a restricciones.

José Antonio Menéndez Fernández (1984)

Trabajos de Estadística e Investigación Operativa

This paper shows the statistics that define the likelihood ratio tests about the mean of a k-dimensional normal population, when the hypotheses to test are H0: θ = 0; H0*: θ ∈ τφ; H1: θ ∈ τ; H2: θ ∈ Rk, being τ a closed and poliedric convex cone in Rk, and τφ the minima dimension face in τ.It is proved that the obtained statistics distributions are certain combinations of chi-squared distributions, when θ = 0.At last, it is proved that the power functions of the tests satisfy some desirable properties....

Tests for profile analysis based on two-step monotone missing data

Mizuki Onozawa, Sho Takahashi, Takashi Seo (2013)

Discussiones Mathematicae Probability and Statistics

In this paper, we consider profile analysis for the observations with two-step monotone missing data. There exist three interesting hypotheses - the parallelism hypothesis, level hypothesis, and flatness hypothesis - when comparing the profiles of some groups. The T²-type statistics and their asymptotic null distributions for the three hypotheses are given for two-sample profile analysis. We propose the approximate upper percentiles of these test statistics. When the data do not have missing observations,...

Tests in weakly nonlinear regression model

Lubomír Kubáček, Eva Tesaříková (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In weakly nonlinear regression model a weakly nonlinear hypothesis can be tested by linear methods if an information on actual values of model parameters is at our disposal and some condition is satisfied. In other words we must know that unknown parameters are with sufficiently high probability in so called linearization region. The aim of the paper is to determine this region.

Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions

František Rublík (2001)

Kybernetika

Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level provided that the population characteristic roots are distinct and the covariance matrices of certain quadratic...

The relative potency of two preparations applied in the supplemented block design with multivariate responses.

Zofia Hanusz (1999)

Qüestiió

The method of point and interval estimation of the relative potency of two preparations: Standard and Test in the multivariate case is presented. General formulae for testing the hypotheses about the parallelism of regression lines and the relative potency have been adopted to experiments in which doses of preparations are applied in the supplemented block designs. The designs of this kind, with two groups of treatments, the first group comprising the doses of the Standard preparation and the second...

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