Nonparametric Conditional Inference for Regression Coefficients with Application to Configural Polysampling

TL;DR

This paper develops a nonparametric method for conditional inference on regression coefficients, using ancillary statistics and kernel density estimators, and applies it to robust estimation via configural polysampling.

Contribution

It introduces a nonparametric conditional inference framework for regression coefficients and extends configural polysampling to this setting, ensuring robustness and accurate coverage.

Findings

Conditional asymptotic normality of estimators established

Kernel plug-in approach yields accurate confidence intervals

Extension of configural polysampling to nonparametric context

Abstract

We consider inference procedures, conditional on an observed ancillary statistic, for regression coefficients under a linear regression setup where the unknown error distribution is specified nonparametrically. We establish conditional asymptotic normality of the regression coefficient estimators under regularity conditions, and formally justify the approach of plugging in kernel-type density estimators in conditional inference procedures. Simulation results show that the approach yields accurate conditional coverage probabilities when used for constructing confidence intervals. The plug-in approach can be applied in conjunction with configural polysampling to derive robust conditional estimators adaptive to a confrontation of contrasting scenarios. We demonstrate this by investigating the conditional mean squared error of location estimators under various confrontations in a simulation study, which successfully extends configural polysampling to a nonparametric context.