Based on an omnibus likelihood ratio test statistic for the equality of several variance-covariance matrices following the complex Wishart distribution and a factorization of this test statistic with associated p-values, change analysis in a time series of multilook, polarimetric SAR data in the covariance matrix representation is carried out. The omnibus test statistic and its factorization de...

Testing for homogeneity in finite mixture models has been investigated by many authors. The asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to use in practice. In this paper we propose a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family. The modified LRT has a χ2-type null limiting distributio...

While on one hand, the exact distribution of the likelihood ratio test statistic for testing the equality of several variance-covariance matrices, as it also happens with several other likelihood ratio test statistics used in Multivariate Statistics, has a non-manageable form, which does not allow for the computation of quantiles, even for a small number of variables, on the other hand the asym...

This paper studies properties of the likelihood ratio (LR) tests associated with the limited information maximum likelihood (LIML) estimators in a structural form estimation when the number of instrumental variables is large. Two types of asymptotic theories are developed to approximate the distribution of the likelihood ratio (LR) statistic under the null hypothesis H0 : β = β0: a (large sampl...

We consider the tting of a g-component normal mixture to multivariate data. The problem is to test whether g is equal to some speciied value versus some speciied alternative value. This problem would arise, for example, in the context of a cluster analysis eeected by a normal mixture model, where the decision on the number of clusters is undertaken by testing for the smallest value of g compati...

We show the software SOLOMON is improved by using the likelihood ratio instead of an ad hoc statistic. CODE:  github.com/eriqande/solidmon/releases/tag/v0.1-bioinformatics

The Inverse Gaussian (IG) distribution is commonly introduced to model and examine right skewed data having positive support. When applying the IG model, it is critical to develop efficient goodness-of-fit tests. In this article, we propose a new test statistic for examining the IG goodness-of-fit based on approximating parametric likelihood ratios. The parametric likelihood ratio methodology i...

Composite likelihood may be useful for approximating likelihood based inference when the full likelihood is too complex to deal with. Stemming from a misspecified model, inference based on composite likelihood requires suitable corrections. Here we focus on the composite likelihood ratio statistic for a multidimensional parameter of interest, and we propose a parameterization invariant adjustme...

In the last lecture we saw that the likelihood ratio statistic was optimal for testing between two simple hypotheses. The test simply compares the likelihood ratio to a threshold. The “optimal” threshold is a function of the prior probabilities and the costs assigned to different errors. The choice of costs is subjective and depends on the nature of the problem, but the prior probabilities must...

This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The is applicable particular X-ray spectra situations where Poisson log-likelihood, or Cash goodness-of-fit statistic, indicate poor fit that attributable overdispersion Overdispersion data treated as an intrinsic model variance can be estimated from best-fit model, using Cmin stat...