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Asymptotic Behaviors of Some Measures of Accuracy in Nonparametric Curve Estimation with Dependent Observations

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  • Kim, T. Y.
  • Cox, D. D.

Abstract

Under the i.i.d. condition, Marron and Härdle (1986, J. Multivariate Anal.20 91-113) showed that quadratic measures of errors for nonparametric kernel estimates are asymptotically equivalent, and Hall (1984, J. Multivariate Anal.14 1-16) investigated their convergence rates. In this article, we extend their results to the dependent case. In addition, the effect of dimension on the convergence rates will be discussed.

Suggested Citation

  • Kim, T. Y. & Cox, D. D., 1995. "Asymptotic Behaviors of Some Measures of Accuracy in Nonparametric Curve Estimation with Dependent Observations," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 67-93, April.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:67-93
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    Cited by:

    1. Estévez-Pérez, Graciela, 2002. "On convergence rates for quadratic errors in kernel hazard estimation," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 231-241, April.
    2. Xia, Yingcun & Li, W. K., 2002. "Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 265-287, November.
    3. Tae Kim & Zhi-Ming Luo & Chiho Kim, 2011. "The central limit theorem for degenerate variable -statistics under dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 683-699.
    4. Zudi Lu & Dag Johan Steinskog & Dag Tjøstheim & Qiwei Yao, 2009. "Adaptively varying‐coefficient spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 859-880, September.

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