On the multivariate asymptotic distribution of sequential Chi-square statistics

On the Multivariate Asymptotic Distribution of Sequential Chi-square Statistics

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-square difference tests are asymp...

Computing and approximating multivariate chi-square probabilities

We consider computational methods for evaluating and approximating multivariate chisquare probabilities in cases where the pertaining correlation matrix or blocks thereof have a low-factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a...

Chi-Square Statistics with Multiple Imputation

On Some Central and Non - Central Multivariate Chi - Square Distributions

Let R be a non-singular m-factorial correlation matrix, i.e. R = D + AA0 with a diagonal matrixD > 0 and a not necessarily de nite matrix AA0 of the minimal possible rank m. From an expression for the general non-central multivariate distribution function with the accompanying correlation matrix R some simpler cases are derived: The p-variate central -distribution with q degrees of freedom is g...

On the multi _ chi-square tests and their data complexity

Chi-square tests are generally used for distinguishing purposes; however when they are combined to simultaneously test several independent variables, extra notation is required. In this study, the chi-square statistics in some previous works is revealed to be computed half of its real value. Therefore, the notion of Multi _ Chi-square tests is formulated to avoid possible future confusions. In ...