摘要

For the semiparametric regression model: Y-( j) (x(in), t(in)) = t(in)beta + g(x(in)) + e((j)) (x(in)), 1 <= j <= m, 1 <= i <= n, where t(in) is an element of R and x(in) is an element of R-p are known to be nonrandom, g is an unknown continuous function on a compact set A in R-P, e (j) (x(in)) are rho*-mixing random errors with mean zero, Y-(j) (x(in), t(in)) represent the j-th response variables which are observable at points x(in), t(in). In this paper, we study the strong consistency and r-th (1 < r <= 2) mean consistency for the estimators beta(m,n) and g(m,n) of beta and g, respectively. The results obtained in this paper improve and extend the corresponding ones for rho*-mixing random variables and other dependent sequences.