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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.
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.
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.
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....
En este artículo se construyen varios tests sobre el parámetro de la distribución exponencial, basados en la distancia de Rao. Los tests así desarrollados son comparados con los tests básicos de la inferencia estadística.
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,...
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.
In the paper, a new approach to construction test for independenceof two-dimensional normally distributed random vectors is given under the assumption that the ratio of the variances is known. This test is uniformly better than the t-Student test. A comparison of the power of these two tests is given. A behaviour of this test forsome ε-contamination of the original model is also shown. In the general case when the variance ratio is unknown, an adaptive test is presented. The equivalence between...
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...
Finite mixture modelling of class-conditional distributions is a standard method in a statistical pattern recognition. This paper, using bag-of-words vector document representation, explores the use of the mixture of multinomial distributions as a model for class-conditional distribution for multiclass text document classification task. Experimental comparison of the proposed model and the standard Bernoulli and multinomial models as well as the model based on mixture of multivariate Bernoulli distributions...
For the analysis of square contingency tables, Caussinus (1965) proposed the quasi-symmetry model and gave the theorem that the symmetry model holds if and only if both the quasi-symmetry and the marginal homogeneity models hold. Bishop, Fienberg and Holland (1975, p.307) pointed out that the similar theorem holds for three-way tables. Bhapkar and Darroch (1990) gave the similar theorem for general multi-way tables. The purpose of this paper is (1) to review some topics on various symmetry models,...
This paper highlights advantageous properties of the Bhattacharyya metric over the chi-squared statistic for comparing frequency distributed data. The original interpretation of the Bhattacharyya metric as a geometric similarity measure is reviewed and it is pointed out that this derivation is independent of the use of the Bhattacharyya measure as an upper bound on the probability of misclassification in a two-class problem. The affinity between the Bhattacharyya and Matusita measures is described...
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