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October 1999 Nonparametric estimation of quadratic regression functionals
Li-Shan Huang, Jianqing Fan
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Bernoulli 5(5): 927-949 (October 1999).


Quadratic regression functionals are important for bandwidth selection of nonparametric regression techniques and for nonparametric goodness-of-fit test. Based on local polynomial regression, we propose estimators for weighted integrals of squared derivatives of regression functions. The rates of convergence in mean square error are calculated under various degrees of smoothness and appropriate values of the smoothing parameter. Asymptotic distributions of the proposed quadratic estimators are considered with the Gaussian noise assumption. It is shown that when the estimators are pseudo-quadratic (linear components dominate quadratic components), asymptotic normality with rate n-1/2 can be achieved.


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Li-Shan Huang. Jianqing Fan. "Nonparametric estimation of quadratic regression functionals." Bernoulli 5 (5) 927 - 949, October 1999.


Published: October 1999
First available in Project Euclid: 12 February 2007

zbMATH: 0938.62041
MathSciNet: MR1715445

Keywords: asymptotic normality , equivalent kernel , local polynomial regression

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

Vol.5 • No. 5 • October 1999
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