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.