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Symmetrized Multivariate k -NN Estimators

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  • Yanqin Fan
  • Ruixuan Liu

Abstract

In this article, we propose a symmetrized multivariate k -NN estimator for the conditional mean and for the conditional distribution function. We establish consistency and asymptotic normality of each estimator. For the estimator of the conditional distribution function, we also establish the weak convergence of the conditional empirical process to a Gaussian process. Compared with the corresponding kernel estimators, the asymptotic distributions of our k -NN estimators do not depend on the existence of the marginal probability density functions of the covariate vector. A small simulation study compares the finite sample performance of our symmetrized multivariate k -NN estimator with the Nadaraya-Watson kernel estimator for the conditional mean.

Suggested Citation

  • Yanqin Fan & Ruixuan Liu, 2015. "Symmetrized Multivariate k -NN Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 828-848, December.
  • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:828-848
    DOI: 10.1080/07474938.2014.956590
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    References listed on IDEAS

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    1. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    2. Carroll, R. J. & Härdle, W., 1989. "Symmetrized nearest neighbor regression estimates," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 315-318, February.
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    Cited by:

    1. Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.

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