Acta mathematica scientia,Series B ›› 1996, Vol. 16 ›› Issue (S1): 57-69.
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Shi Peide, Zheng Zhongguo
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Abstract: Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)}, we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)|where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order r, it is shown that the optimal global convergence rate, n-r/(2r+J), is attained by the L1-norm based estimators.
Key words: Least absolute deviation, nonparametric regresion, tensor product of Bsplines
Shi Peide, Zheng Zhongguo. ROBUST ESTIMATES IN MULTIVARIATE NONPARAMETRIC REGRESSION VIA LEAST ABSOLUTE DEVIATIONS[J].Acta mathematica scientia,Series B, 1996, 16(S1): 57-69.
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