Geometric Understanding of Likelihood Ratio Statistics

Geometric Understanding of Likelihood Ratio Statistics

It is well-known that twice a log-likelihood ratio statistic follows asymptotically a -distribution. The result is usually understood and proved via Taylor's expansions of likelihood functions and by assuming asymptotic normality of maximum likelihood estimators. We contend that more fundamental insights can be obtained for likelihood ratio statistics: the Wilks type of results hold as long as ...

Generalized Likelihood Ratio Statistics

Adjusting Composite Likelihood Ratio Statistics

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...

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...

On Multivariate Likelihood Ratio Ordering among Generalized Order Statistics and their Spacings

The most of the results obtained about stochastic properties of generalized order statistics and their spacings in the literature are based on equal model parameters. In this paper, with less restrictive conditions on the model parameters, we prove some new multivariate likelihood ratio ordering results between two sub-vectors of GOS's as well as two sub-vectors of $p$-spacings based on two con...