Wilks on Hemianæsthesia

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 ...

Some Nonparametric Generalizations of Wilks' Tests for . . .

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...

A Wilks Theorem for the Censored Empirical Likelihood of Means

In this note we give a proof of the Wilks theorem for the empirical likelihood ratio for the right censored data, when the hypothesis are formulated in terms of p estimating equations or mean functions. In particular we show that the empirical likelihood ratio test statistic is equal to a quadratic form similar to a Hotelling’s T 2 statistic, plus a small error.

Robustness of Wilks’ Conservative Estimate of Confidence Intervals

The striking generality and simplicity of Wilks’ method has made it popular for quantifying modeling uncertainty. A conservative estimate of the confidence interval is obtained from a very limited set of randomly drawn model sample values, with probability set by the assigned so-called stability. In contrast, the reproducibility of the estimated limits, or robustness, is beyond our control as i...