Sharp bounds on quasiconvex moments of generalized order statistics.
Some applications of the matrix Haffian in connection with differentiable matrix functions of a central Wishart variate.
In this paper we revisit Haff's seminal work on the matrix Haffian as we proposed to call it. We review some results, and give new derivations. Use is made of the link between the matrix Haffian ∇F and the differential of the matrix function, dF.
Some properties of beta functions and the distribution for the product of independent beta random variables.
Products of independent beta random variables appear in a large number of problems in multivariate statistical analysis. In this paper we show how a convenient factorial expansion of gamma ratios can be suitably used in deriving the exact density for a product of independent beta random variables. Possible applications of this result for obtaining the exact densities of the likelihood ratio criteria for testing hypotheses in the multinormal case are also pointed out. For the sake of illustration,...
Stochastic comparison of multivariate random sums
We establish preservation results for the stochastic comparison of multivariate random sums of stationary, not necessarily independent, sequences of nonnegative random variables. We consider convex-type orderings, i.e. convex, coordinatewise convex, upper orthant convex and directionally convex orderings. Our theorems generalize the well-known results for the stochastic ordering of random sums of independent random variables.
Structural breaks in dependent, heteroscedastic, and extremal panel data
New statistical procedures for a change in means problem within a very general panel data structure are proposed. Unlike classical inference tools used for the changepoint problem in the panel data framework, we allow for mutually dependent panels, unequal variances across the panels, and possibly an extremely short follow up period. Two competitive ratio type test statistics are introduced and their asymptotic properties are derived for a large number of available panels. The proposed tests are...
Testing block sphericity of a covariance matrix.
Testing hypotheses in universal models
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 of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions
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 Bayes approach in multiple autoregressive series
The Bivariate Non-central Negative Binomial Distributions.
The generalized FGM distribution and its application to stereology of extremes
The generalized FGM distribution and related copulas are used as bivariate models for the distribution of spheroidal characteristics. It is shown that this model is suitable for the study of extremes of the 3D spheroidal particles observed in terms of their random planar sections.
The likelihood ratio test for general mixture models with or without structural parameter
This paper deals with the likelihood ratio test (LRT) for testing hypotheses on the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRT statistics under some conditions that are proved to be almost necessary. A detailed solution is given for two testing problems: the test of a single distribution against any mixture, with application to Gaussian, Poisson and binomial distributions; the test of the number of populations...
The Mean and Variance of the Likelihood Ratio Criterion for the Multidimensional Distribution.
Transformations groups of the Andersson-Perlman cone.
Variables finitas condicionalmente especificadas.
En este trabajo se estudia la existencia y unicidad de vectores bidimensionales de variables discretas con recorrido finito, cuando se fijan sus distribuciones condicionadas. Para ello, tras repasar la literatura existente sobre el tema, proporcionamos diversos resultados que relacionan diversos temas de álgebra matricial, especialmente la descomposición singular, con el problema que nos ocupa.
Wishart distributions in the multivariate Gauss-Markoff model with singular covariance matrix
This paper concerns generalized quadratic forms for the multivariate case. These forms are used to test linear hypotheses of parameters for the multivariate Gauss-Markoff model with singular covariance matrix. Distributions and independence of these forms are proved.
Współczynnik zależności monotonicznej z próbki (II)
Некоторые вероятностные свойства обобщенной статистики омега-квадрат
О гипотезе многовыборочной сферичности
Один вариант обобщенной статистики oмега-квадрат