NONPARAMETRIC ESTIMATES OF THE NUISANCE PARAMETER IN THE LAD TESTS

The L1-norm method in linear regression model has attracted considerable attention in recent years. Some L1-norm based techniques for testing linear hypothesis have been proposed and investigated. A nuisance parameter involved in those test statistics needs to be estimated effectively, although several promising estimates have been proposed in the literature. We propose several nonparametric estimates in this paper and prove the strong consistency. Our methods are based on the density estimation method developed by Rosenblatt (1956), Parzen (1962) and others and the conditional density estimation developed by Zhao and Liu (1985) and Liu (1986).