Abstract

Likelihood ratio methods are a central tool in statistical inference, but their classical justification is largely asymptotic and local. In regular parametric models, Wilks’ theorem predicts a universal chi-square behavior, suggesting that likelihood ratio confidence sets should behave as if they had a simple dimension-dependent number of degrees of freedom. I will discuss a nonasymptotic theory for the likelihood ratio in logistic regression. The main result shows that, under arbitrary fixed designs, the worst-case finite-sample behavior can be larger than the classical Wilks prediction by a logarithmic factor, and that this loss is unavoidable. The bound holds uniformly over all design matrices and all true parameters, and does not require the maximum likelihood estimator to exist.

About the speaker

Prof. Nikita Zhivotovskiy is an Assistant Professor in the Department of Statistics at the University of California, Berkeley. His research interests lie at the intersection of mathematical statistics, probability, and learning theory. His work focuses on understanding what can be learned from data under minimal assumptions, with an emphasis on finite-sample, non-asymptotic, and distribution-free guarantees for statistical and machine learning problems.