The Bivariate Non-central Negative Binomial Distributions.
The conditional distribution of random errors for given observed values with application to factor analysis
The correloid
The determination of factors in linear models of factor analysis
The author shows that a decomposition of a covariance matrix implies the corresponding model, i.e. the existence of factors such that is true. The result is applied to the general linear model of factor analysis. A procedure for computing the factor score is proposed.
The ... -Divergence Statistic in Bivariate Multinomial Populations Including Stratification.
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 importance of being the upper bound in the bivariate family.
Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric...
The Large-Sample Power of the x Test fox Multidimensional Contingency Tables.
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 likelihood ratio test for the number of components in a mixture with Markov regime
The likelihood ratio test for the number of components in a mixture with Markov regime
We study the LRT statistic for testing a single population i.i.d. model against a mixture of two populations with Markov regime. We prove that the LRT statistic converges to infinity in probability as the number of observations tends to infinity. This is a consequence of a convergence result of the LRT statistic for a subproblem where the parameters are restricted to a subset of the whole parameter set.
The linear model with variance-covariance components and jackknife estimation
Let be a biased estimate of the parameter based on all observations , , and let () be the same estimate of the parameter obtained after deletion of the -th observation. If the expectation of the estimators and are expressed as where is a known sequence of real numbers and is a function of , then this system of equations can be regarded as a linear model. The least squares method gives the generalized jackknife estimator. Using this method, it is possible to obtain the unbiased...
The locally best estimators of the first and second order parameters in epoch regression models
The Lukacs-Olkin-Rubin theorem on symmetric cones through Gleason's theorem
We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Wesołowski, Studia Math. 152 (2002), 147-160]. The main tool is a new solution of the Olkin-Baker functional equation on symmetric cones, under the assumption of continuity of respective functions. It was possible thanks to the use of Gleason's theorem.
The Lukacs-Olkin-Rubin theorem without invariance of the "quotient"
The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental reason...
The Mean and Variance of the Likelihood Ratio Criterion for the Multidimensional Distribution.
The missing early history of contingency tables
The most significant interaction in a contingency table
The multiple regression model where independent variables are measured unprecisely.
The Occurrence of Outliers in the Explanatory Variable Considered in an Errors-in-Variables Framework.