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Probabilities of maximal deviations for nonparametric regression function estimates

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  • Johnston, Gordon J.
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    Abstract

    Let (X, Y) have regression function m(x) = E(Y X = x), and let X have a marginal density f1(x). We consider two nonparameteric estimates of m(x): the Watson estimate when f1 is known and the Yang estimate when f1 is known or unknown. For both estimates the asymptotic distribution of the maximal deviation from m(x) is proved, thus extending results of Bickel and Rosenblatt for the estimation of density functions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 12 (1982)
    Issue (Month): 3 (September)
    Pages: 402-414

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    Handle: RePEc:eee:jmvana:v:12:y:1982:i:3:p:402-414

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    Related research

    Keywords: Density estimates nonparemetric regression estimates maximal deviations Gaussian processes;

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    Cited by:
    1. J. Cristóbal & J. Ojeda & J. Alcalá, 2004. "Confidence bands in nonparametric regression with length biased data," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(3), pages 475-496, September.
    2. Hidalgo, J., 2008. "Specification testing for regression models with dependent data," Journal of Econometrics, Elsevier, vol. 143(1), pages 143-165, March.
    3. Efang Kong & Oliver Linton & Yingcun Xia, 2011. "Global Bahadur representation for nonparametric censored regression quantiles and its applications," CeMMAP working papers CWP33/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Wolfgang Karl Härdle & Ya'acov Ritov & Weining Wang, 2013. "Tie the straps: uniform bootstrap confidence bands for bounded influence curve estimators," SFB 649 Discussion Papers SFB649DP2013-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Norberto Rodríguez & Patricia Siado, 2003. "Un Pronóstico No Paramétrico De La Inflación Colombiana," BORRADORES DE ECONOMIA 003691, BANCO DE LA REPÚBLICA.
    6. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Härdle, 2014. "Confidence Corridors for Multivariate Generalized Quantile Regression," SFB 649 Discussion Papers SFB649DP2014-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Javier Hidalgo, 2007. "Specification testing for regression models with dependent data," LSE Research Online Documents on Economics 6799, London School of Economics and Political Science, LSE Library.
    8. Zhao, Zhibiao, 2011. "Nonparametric model validations for hidden Markov models with applications in financial econometrics," Journal of Econometrics, Elsevier, vol. 162(2), pages 225-239, June.

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