Parametric Bootstrap Inference for Stratified Models With High-Dimensional Nuisance Specifications

Inference about a scalar parameter of interest typically relies on the asymptotic normality common likelihood pivots, such as signed root, score and Wald statistics. Nevertheless, resulting inferential procedures have been known to perform poorly when dimension nuisance is large relative sample size information parameters limited. In cases, use analytical modifications root recover performance. It proved here that parametric bootstrap standard pivots results in accurate inferences do stratified models with stratum specific parameters. We focus challenging case where number strata increases fast or faster than samples size. also shown this equivalence holds regardless whether constrained unconstrained used. This contrast space fixed size, correct inference higher-order does. Large scale simulation experiments support theoretical findings demonstrate excellent performance some extreme modelling scenarios.