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Efficient Bandwidth Selection in Non‐parametric Regression
Author(s) -
PREWITT KATHRYN A.
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00319
Subject(s) - mathematics , estimator , bandwidth (computing) , kernel regression , parametric statistics , kernel density estimation , regression function , polynomial regression , kernel (algebra) , binary number , regression , rate of convergence , mathematical optimization , nonparametric regression , statistics , computer science , discrete mathematics , computer network , channel (broadcasting) , arithmetic
In this paper we use non‐parametric local polynomial methods to estimate the regression function, m ( x ). Y may be a binary or continuous response variable, and X is continuous with non‐uniform density. The main contributions of this paper are the weak convergence of a bandwidth process for kernels of order (0, k ), k =2 j , j ≥1 and the proposal of a local data‐driven bandwidth selection method which is particularly beneficial for the case when X is not distributed uniformly. This selection method minimizes estimates of the asymptotic MSE and estimates the bias portion in an innovative way which relies on the order of the kernel and not estimation of m 2 ( x ) directly. We show that utilization of this method results in the achievement of the optimal asymptotic MSE by the estimator, i.e. the method is efficient. Simulation studies are provided which illustrate the method for both binary and continuous response cases.