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Multivariate Local Polynomial Kernel Estimators: Leading Bias and Asymptotic Distribution

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  • Jingping Gu
  • Qi Li
  • Jui-Chung Yang

Abstract

Masry (1996b) provides estimation bias and variance expression for a general local polynomial kernel estimator in a general multivariate regression framework. Under smoother conditions on the unknown regression function and by including more refined approximation terms than that in Masry (1996b), we extend the result of Masry (1996b) to obtain explicit leading bias terms for the whole vector of the local polynomial estimator. Specifically, we derive the leading bias and leading variance terms of nonparametric local polynomial kernel estimator in a general nonparametric multivariate regression model framework. The results can be used to obtain optimal smoothing parameters in local polynomial estimation of the unknown conditional mean function and its derivative functions.

Suggested Citation

  • Jingping Gu & Qi Li & Jui-Chung Yang, 2015. "Multivariate Local Polynomial Kernel Estimators: Leading Bias and Asymptotic Distribution," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 979-1010, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:979-1010
    DOI: 10.1080/07474938.2014.956615
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    References listed on IDEAS

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    1. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
    2. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    3. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    4. Liu, Zhenjun & Stengos, Thanasis & Li, Qi, 2000. "Nonparametric model check based on local polynomial fitting," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 327-334, July.
    5. Li, Dong & Li, Qi, 2010. "Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters," Journal of Econometrics, Elsevier, vol. 157(1), pages 179-190, July.
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    Cited by:

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    2. Neumeyer, Natalie & Noh, Hohsuk & Van Keilegom, Ingrid, 2014. "Heteroscedastic semiparametric transformation models: estimation and testing for validity," LIDAM Discussion Papers ISBA 2014047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Andrea Meilán-Vila & Mario Francisco-Fernández & Rosa M. Crujeiras & Agnese Panzera, 2021. "Nonparametric multiple regression estimation for circular response," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 650-672, September.
    4. Maria Grith & Wolfgang K. Härdle & Alois Kneip & Heiko Wagner, 2016. "Functional Principal Component Analysis for Derivatives of Multivariate Curves," SFB 649 Discussion Papers SFB649DP2016-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    6. Shi, Jianhong & Bai, Xiuqin & Song, Weixing, 2020. "Nonparametric regression estimate with Berkson Laplace measurement error," Statistics & Probability Letters, Elsevier, vol. 166(C).
    7. Chan Shen, 2019. "Recursive Differencing for Estimating Semiparametric Models," Departmental Working Papers 201903, Rutgers University, Department of Economics.

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