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
