Optimal Gwbal Rates of Covergence in Partly Linear Models
نویسنده
چکیده
Let (X, Z, Y) denote a random vector such that Z and Y are real-valued, and X E ]Rd. Consider the partly linear regression function E(Y I Z, X) = (3Z + ¢(X), where (3 is an unknown parameter, and 4>(') is a smooth function on Rd. Suppose that 4>(') has a bounded kth derivative. Under appropriate conditions, it will be shown that the local polynomial based estimate achieve the usual optimal L2 and L oo rates of convergence given by n-k/(2k+d) and (log n/n)k/(2k+d), respectively.
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تاریخ انتشار 1996