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We consider inference procedures, conditional on an observed ancillarystatistic, for regression coefficients under a linear regression setup wherethe unknown error distribution is specified nonparametrically. We establishconditional asymptotic normality of the regression coefficient estimators underregularity conditions, and formally justify the approach of plugging inkernel-type density estimators in conditional inference procedures. Simulationresults show that the approach yields accurate conditional coverageprobabilities when used for constructing confidence intervals. The plug-inapproach can be applied in conjunction with configural polysampling to deriverobust conditional estimators adaptive to a confrontation of contrastingscenarios. We demonstrate this by investigating the conditional mean squarederror of location estimators under various confrontations in a simulationstudy, which successfully extends configural polysampling to a nonparametriccontext.

Nonparametric Conditional Inference for Regression Coefficients with Application to Configural Polysampling