MINIMUM DISTANCE REGRESSION MODEL CHECKINGWITH BERKSON MEASUREMENT ERRORS

摘要

Lack-of-fit testing of a regression model with Berkson measurement er-ror has not been discussed in the literature to date. To fill this void, we pro-pose a class of tests based on minimized integrated square distances betweena nonparametric regression function estimator and the parametric model be-ing fitted. We prove asymptotic normality of these test statistics under thenull hypothesis and that of the corresponding minimum distance estimatorsunder minimal conditions on the model being fitted. We also prove consis-tency of the proposed tests against a class of fixed alternatives and obtaintheir asymptotic power against a class of local alternatives orthogonal to thenull hypothesis. These latter results are new even when there is no measure-ment error. A simulation that is included shows very desirable finite samplebehavior of the proposed inference procedures.