Bernoulli

  • Bernoulli
  • Volume 5, Number 5 (1999), 927-949.

Nonparametric estimation of quadratic regression functionals

Li-Shan Huang and Jianqing Fan

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Abstract

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.

Article information

Source
Bernoulli, Volume 5, Number 5 (1999), 927-949.

Dates
First available in Project Euclid: 12 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1171290405

Mathematical Reviews number (MathSciNet)
MR1715445

Zentralblatt MATH identifier
0938.62041

Keywords
asymptotic normality equivalent kernel local polynomial regression

Citation

Huang, Li-Shan; Fan, Jianqing. Nonparametric estimation of quadratic regression functionals. Bernoulli 5 (1999), no. 5, 927--949. https://projecteuclid.org/euclid.bj/1171290405


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