Nonparametric Conditional Inference for Regression Coefficients with Application to Configural Polysampling

Details Nonparametric Conditional Inference for Regression Coefficients with Application to Configural Polysampling Nonparametric Conditional Inference for Regression Coefficients with Application to Configural Polysampling

2007-10-30

arxiv.org/abs/0710.5675v1

Statistics

Methodology

Scientific paper

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.

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