Lack-of-fit testing of a regression model with response missing at random

This paper proposes a class of lack-of-fit tests for fitting a linear regression model when some response variables are missing at random. These tests are based on a class of minimum integrated square distances between a kernel type estimator of a regression function and the parametric regression function being fitted. These tests are shown to be consistent against a large class of fixed alternatives. The corresponding test statistics are shown to have asymptotic normal distributions under null hypothesis and a class of nonparametric local alternatives. Some simulation results are also presented.

► We fitted a linear regression model when response variables are missing at random.
► Data set is completed by imputation method.
► Lack-of-fit tests are based on minimum distance method.
► These tests are consistent against a large class of fixed alternatives.
► Test statistics are asymptotic normal under null hypothesis and local alternatives.