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Abstract: Consider the mixed-effect coefficient semiparametric regression model Z=X'α+Y'β+g(T)+e, where X, Y and T are random vectors on R^p×R^q×[0,1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=∑), g(.) is an unknown function on [0,1], e is a random error with mean zero and variance σ², and (X,Y,T) and (β,e), β and e are mutually independent. We estimate α, b and g(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α, b have asymptotic normality and obtain the best convergence rate n^−1/3 for the estimation of g(.).

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