ROBUST　ESTIMATES　IN　MULTIVARIATE　NONPARAMETRIC　REGRESSION　VIA　LEAST　ABSOLUTE　 DEVIATIONS

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 ∑|Yi-g(Xi)| where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order...

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Bibliographic Details
Published inActa mathematica scientia Vol. 16; no. S1; pp. 57 - 69
Main Author 旋沛德 郑忠国
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 1996
Subjects
absolute
Bsplines
deviation
Least
Least absolute deviation
nonparametric
nonparametric regresion
product
regresion
tensor
tensor product of B-splines
tensor product of B-splines
Least absolute deviation
nonparametric regresion
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Summary: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 ∑|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.
Bibliography:42-1227/O
Shi Peide; Zheng Zhongguo(Department of Probability and Statistics, Peking University, Beijing 100871, China)
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(17)30817-2