Far East Journal of Theoretical Statistics
Volume 4, Issue 2, Pages 257 - 284
(December 2000)
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NONLINEAR WAVELET ESTIMATION OF CONDITIONAL MEAN AND
CONDITIONAL VARIANCE FUNCTIONS IN STOCHASTIC REGRESSION
Heung Wong (Hong Kong),Wai Cheung Ip (Hong Kong) and Yuan Li (China)
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Abstract: Stochastic regression model with unknown conditional
mean and conditional variance is considered in this
paper. Under mild conditions, we propose nonlinear
wavelet estimators of these functions based on local
polynomial and wavelet thresholding. It is shown that
the wavelet estimators attain the optimal convergence
rate in a ball of Besov space. The adaptive nonlinear
wavelet estimators with nearly optimal convergence
rate in a ball of Besov space are also developed. |
Keywords and phrases: local polynomial, conditional mean,
conditional variance, optimal convergence rate,
threshold, wavelets. |
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