TY - JOUR
T1 - Robust estimation of nonparametric function via addition sequence
AU - Wang, Wen Wu
AU - Shen, Wei
AU - Tong, Tiejun
N1 - Funding Information:
We would like to thank two anonymous reviewers and associate editor for their constructive comments on improving the quality of the paper. Wang’s work is support by the fund XKJJC201901 of Qufu Normal University, China .
PY - 2021/3
Y1 - 2021/3
N2 - In this paper, we propose a robust method for the estimation of regression function. By symmetric addition, we change platykurtic errors into leptokurtic errors; and then estimate the nonparametric function by the local polynomial least absolute deviation regression. Different from the local polynomial least squares estimator, the new estimator is robust for outliers and heavy-tailed errors even if the error variance does not exist; different from the usual local polynomial least absolute deviation estimator and the composite quantile regression estimator, it does not depend on the finite density values at chosen quantile points, but relies on the expectation of the error density. To improve the finite sample performance, two bias-reduced versions are further proposed under different smoothness conditions. For the equidistant designs, the asymptotic properties are established. In simulations, the new estimator has the less mean square errors than its main competitors in the presence of platykurtic and heavy-tailed errors.
AB - In this paper, we propose a robust method for the estimation of regression function. By symmetric addition, we change platykurtic errors into leptokurtic errors; and then estimate the nonparametric function by the local polynomial least absolute deviation regression. Different from the local polynomial least squares estimator, the new estimator is robust for outliers and heavy-tailed errors even if the error variance does not exist; different from the usual local polynomial least absolute deviation estimator and the composite quantile regression estimator, it does not depend on the finite density values at chosen quantile points, but relies on the expectation of the error density. To improve the finite sample performance, two bias-reduced versions are further proposed under different smoothness conditions. For the equidistant designs, the asymptotic properties are established. In simulations, the new estimator has the less mean square errors than its main competitors in the presence of platykurtic and heavy-tailed errors.
KW - Differenced method
KW - Median smoothing
KW - Platykurtic and heavy-tailed errors
KW - Robust nonparametric function estimation
UR - http://www.scopus.com/inward/record.url?scp=85090193127&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2020.07.007
DO - 10.1016/j.jspi.2020.07.007
M3 - Journal article
AN - SCOPUS:85090193127
SN - 0378-3758
VL - 211
SP - 423
EP - 438
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
ER -