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Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation

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  • Lu, Zhan-Qian

Abstract

Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional kernel estimators, these estimators are often of simpler form and possess some better properties. In this paper, we develop current work on locally weighted regression and generalize locally weighted polynomial fitting to the estimation of partial derivatives in a multivariate regression context. Specifically, for both the regression and partial derivative estimators we prove joint asymptotic normality and derive explicit asymptotic expansions for their conditional bias and conditional convariance matrix (given observations of predictor variables) in each of the two important cases of local linear fit and local quadratic fit.

Suggested Citation

  • Lu, Zhan-Qian, 1996. "Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 187-205, November.
  • Handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:187-205
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    Citations

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    Cited by:

    1. Zhan-Qian Lu, 1999. "Multivariate Local Polynomial Fitting for Martingale Nonlinear Regression Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(4), pages 691-706, December.
    2. Giordano, Francesco & Parrella, Maria Lucia, 2016. "Bias-corrected inference for multivariate nonparametric regression: Model selection and oracle property," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 71-93.
    3. Francesco Giordano & Maria Lucia Parrella, 2014. "Bias-corrected inference for multivariate nonparametric regression: model selection and oracle property," Working Papers 3_232, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    4. Charnigo, Richard & Feng, Limin & Srinivasan, Cidambi, 2015. "Nonparametric and semiparametric compound estimation in multiple covariates," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 179-196.
    5. Francesco Giordano & Soumendra Nath Lahiri & Maria Lucia Parrella, 2014. "GRID for model structure discovering in high dimensional regression," Working Papers 3_231, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    6. Zhang, Wenyang & Lee, Sik-Yum, 2000. "Variable Bandwidth Selection in Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 116-134, July.

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