Linear plus quadratic (LPQ) quasiminimax estimation in the linear regression model

Abstract

If the errors in the linear regression model are assumed to be independent with nonvanishing third and finite fourth moments, then it is possible to improve all linear estimators by so-called linear plus quadratic (LPQ) estimators. These consist of linear and quadratic terms in the endogeneous variable and depend on the unknown moments of the errors which, in general, have to be estimated from the data. In this paper, we will use LPQ estimators for quasiminimax estimation and some related problems. (1991): 62J05, 62C20. Mathematics Subject Classifications