M-Type Regression Splines Involving Time Series
نویسنده
چکیده
Consider a strictly stationary time series Zb =fvalued and Y i real-valued. The nonparametric M-type regression function g 0 () is deened by E(((Y 1 ? g 0 (X 1)) j X 1 = x) = 0. Tensor products of B-splines are adopted to approximate g 0 and a class of M-type regression spline estimators of this function are obtained based on a segment, (X 1 ; Y 1); ; (X n ; Y n), of Z. Suppose that g 0 () is smooth up to order r (> d=2). Under certain regularity conditions, the M-type regression spline estima-tors can achieve the optimal rates of convergence n ?r=(2r+d) in L 2-norms restricted to a compact domain when the spline knots are deterministically given. The M-estimators considered here include Huber's estimator, L 1-norm estimator, regression quantile estimator and L P-norm estimator as special cases. Short title: M-type regression splines.
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