Nonparametric estimation of the discontinuous variance function using adjusted residuals

Title & Authors
Nonparametric estimation of the discontinuous variance function using adjusted residuals
Huh, Jib;

Abstract
In usual, the discontinuous variance function was estimated nonparametrically using a kernel type estimator with data sets split by an estimated location of the change point. Kang et al. (2000) proposed the Gasser-$\small{M{\ddot{u}}ller}$ type kernel estimator of the discontinuous regression function using the adjusted observations of response variable by the estimated jump size of the change point in $\small{M{\ddot{u}}ller}$ (1992). The adjusted observations might be a random sample coming from a continuous regression function. In this paper, we estimate the variance function using the Nadaraya-Watson kernel type estimator using the adjusted squared residuals by the estimated location of the change point in the discontinuous variance function like Kang et al. (2000) did. The rate of convergence of integrated squared error of the proposed variance estimator is derived and numerical work demonstrates the improved performance of the method over the exist one with simulated examples.
Keywords
Change point;jump size;kernel function;residual;variance function;
Language
Korean
Cited by
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