ON B-SPLINE M-ESTIMATORS IN A SEMIPARAMETRIC REGRESSION MODEL
摘要
. This paper deals with M-estimators for a semiparametric regression model Y = X ø fi 0 + g0(T ) + e, where Y is real-valued, T ranges over a nondegenerate compact interval, X 2 R d , e is a random error, fi 0 is a d-vector of parameters to be estimated, and g0 is an unknown smooth function whose mth derivative function satisfies a Holder condition with exponent fl 2 (0; 1]. A B-spline is taken to approximate g0 , the M - estimators of fi and g0 are defined, and their convergence rates are investigated. A Monte Carlo study is carried out. It is shown that when the random errors are normally distributed the M-estimators are as good as least square estimators; however, when the random errors are drawn from a symmetrically contaminated normal distribution the M-estimators are superior to least square estimators; and when the random errors are distributed as Cauchy distribution the M-estimators seem acceptable but the least square estimators behave poorly. It is proved that the B-s...