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Convergence rates for parametric components in a partly linear model. (English) Zbl 0637.62067

Consider the regression model Y i =X i ' β+g(t i )+e i for i=1,···,n. Here g is an unknown Hölder continuous function of known order p in R, β is a k×1 parameter vector to be estimated and e i is an unobserved disturbance. Such a model is often encountered in situations in which there is little real knowledge about the nature of g.

A piecewise polynomial g n is proposed to approximate g. The least- squares estimator β ^ is obtained based on the model Y i =X i ' β+g n (t i )+e i . It is shown that β ^ can achieve the usual parametric rates n -1/2 with the smallest possible asymptotic variance for the case that X and T are correlated.


MSC:
62J05Linear regression
62J10Analysis of variance and covariance
62G99Nonparametric inference
41A15Spline approximation