FUZZY WEIGHTED SCALED COEFFICIENTS IN SEMIPARAMETRIC MODEL

In general, the regressor variables are stochastic, Duan and Li (1987, J. Econometrics, 35, 25-35), Li and Duan (1989, Ann. Statist., 17, 10 09-1052) have been shown that under very general design conditions, th e least squares method can still be useful in estimating the scaled re gression coefficients of the semi-parametric model Y-i = Q(1)(alpha beta X(i);epsilon(i)), i = 1,2,..., n. Here alpha is a constant, beta is a 1 x p row vector, X(i) is a p x 1 column vector of explanatory va riables, epsilon(i) is an unobserved random error and Q(1) is an arbit rary unknown function. When the data set (X(i), Y-i), i = 1, 2,..., n, contains one or several outliers, the least squares method can not pr ovide a consistent; estimator of the scaled coefficients beta. Therefo re, we suggest the ''fuzzy'' weighted least squares method to estimate the scaled coefficients beta for the data set with one or several out liers. It will be shown that the proposed ''fuzzy'' weighted least squ ares estimators are root n-consistent and asymptotically normal under very general design condition. Consistent measurement of the precision for the estimator is also given. Moreover, a limited Monte Carlo simu lation and an example are used to study the practical performance of t he procedures.