Abstract: Consider the regression model y₁=x₁β+g(t₁)+e_i for i=1,2,…, n. Here the design points (x_i,t_i) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of ĝ_n(·) of g(·) including known estimates proposed by Gasser & Muller^[1] is also proposed to be a class of new nearest neighbor estimates of g(·). Based on the nonparametric regression procedures, we investigate a statistic for testing H₀:g=0, and obtain some asymptotic results about estimates.

Key words: Partial linear model, Parametric test, Asmpptotic normality, Nonperametric regression technique