Exact Noncentral Distributions of Wilks' $\Lambda$ and Wilks-Lawley $U$ Criteria as Mixtures of Incomplete Beta Functions: for Three Tests

Some Nonparametric Generalizations of Wilks' Tests for . . .

Wilks’ Factorization of the Complex Matrix Variate Dirichlet Distributions

In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta di...

A high-dimensional Wilks phenomenon

A theorem by Wilks asserts that in smooth parametric density estimation the difference between the maximum likelihood and the likelihood of the sampling distribution converges toward a chi-square distribution where the number of degrees of freedom coincides with the model dimension. This observation is at the core of some goodness-of-fit testing procedures and of some classical model selection ...

Computing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t

In this article, we address the problem of computing the distribution functions that can be expressed as discrete mixtures of continuous distributions. Examples include noncentral chisquare, noncentral beta, noncentral F , noncentral t, and the distribution of squared sample multiple correlation. We illustrate the need for improved algorithms by pointing out situations where existing algorithms...

Generalized Likelihood Ratio Statistics and Wilks Phenomenon

The likelihood ratio theory contributes tremendous success to parametric inferences. Yet, there is no general applicable approach for nonparametric inferences based on function estimation. Maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting. Even if they exist, they are hard to find and can not be optimal as shown in this paper. We intr...