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Weighted Nadaraya-Watson regression estimation

  • Cai, Zongwu

In this article, we study nonparametric estimation of regression function by using the weighted Nadaraya-Watson approach. We establish the asymptotic normality and weak consistency of the resulting estimator for [alpha]-mixing time series at both boundary and interior points, and we show that the weighted Nadaraya-Watson estimator not only preserves the bias, variance, and more importantly, automatic good boundary behavior properties of local linear estimator, but also makes computation fast. Furthermore, the asymptotic minimax efficiency is discussed. Finally, comparisons between weighted Nadaraya-Watson approach and local linear fitting are given.

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 51 (2001)
Issue (Month): 3 (February)
Pages: 307-318

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Handle: RePEc:eee:stapro:v:51:y:2001:i:3:p:307-318
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  1. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
  2. Peter Hall & Rodney C. L. Wolff & Qiwei Yao, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
  3. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
  4. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 73-87, December.
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