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Asymptotic Distribution of Smoothers Based on Local Means and Local Medians under Dependence

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  • Boente, G.
  • Fraiman, R.

Abstract

The asymptotic distribution of k th nearest neighbor regression and autoregression estimates (local means) is obtained for [alpha]-mixing processes. Local medians, as considered by Truong and Stone (1991, Ann. Statist.20 77-97), are also shown to be asymptotically normally distributed.

Suggested Citation

  • Boente, G. & Fraiman, R., 1995. "Asymptotic Distribution of Smoothers Based on Local Means and Local Medians under Dependence," Journal of Multivariate Analysis, Elsevier, vol. 54(1), pages 77-90, July.
    • Handle: RePEc:eee:jmvana:v:54:y:1995:i:1:p:77-90
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    Cited by:

    1. Taoufik Bouezmarni & Abderrahim Taamouti, 2014. "Nonparametric tests for conditional independence using conditional distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 697-719, December.
    2. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2017. "Extreme M-quantiles as risk measures: From L1 to Lp optimization," TSE Working Papers 17-841, Toulouse School of Economics (TSE).
    3. Ruiz-Castillo, Javier, 2012. "From the “European Paradox” to a European Drama in citation impact," UC3M Working papers. Economics we1211, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Jürgen Franke & Peter Mwita & Weining Wang, 2015. "Nonparametric estimates for conditional quantiles of time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 107-130, January.
    5. Marie Hušková & Matúš Maciak, 2017. "Discontinuities in robust nonparametric regression with α-mixing dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 447-475, April.
    6. Chu, Ba & Jacho-Chávez, David T., 2012. "k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA," Econometric Theory, Cambridge University Press, vol. 28(4), pages 769-803, August.
    7. Zongwu Cai & Xian Wang, 2013. "Nonparametric Methods for Estimating Conditional VaR and Expected Shortfall," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

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