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Local Linear Multivariate Regression with Variable Bandwidth in the Presence of Heteroscedasticity

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Listed:
  • Azhong Ye
  • Rob J Hyndman
  • Zinai Li

Abstract

We present a local linear estimator with variable bandwidth for multivariate nonparametric regression. We prove its consistency and asymptotic normality in the interior of the observed data and obtain its rates of convergence. This result is used to obtain practical direct plug-in bandwidth selectors for heteroscedastic regression in one and two dimensions. We show that the local linear estimator with variable bandwidth has better goodness-of-fit properties than the local linear estimator with constant bandwidth, in the presence of heteroscedasticity.

Suggested Citation

  • Azhong Ye & Rob J Hyndman & Zinai Li, 2006. "Local Linear Multivariate Regression with Variable Bandwidth in the Presence of Heteroscedasticity," Monash Econometrics and Business Statistics Working Papers 8/06, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2006-8
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2006/wp8-06.pdf
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    References listed on IDEAS

    as
    1. H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    2. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
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    Cited by:

    1. Jungwoo Kim & Joocheol Kim, 2017. "Nonparametric forecasting with one-sided kernel adopting pseudo one-step ahead data," Working papers 2017rwp-102, Yonsei University, Yonsei Economics Research Institute.
    2. Shim, Jooyong & Hwang, Changha, 2009. "Support vector censored quantile regression under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 912-919, February.
    3. Jooyong Shim & Changha Hwang & Kyungha Seok, 2014. "Composite support vector quantile regression estimation," Computational Statistics, Springer, vol. 29(6), pages 1651-1665, December.

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    More about this item

    Keywords

    Heteroscedasticity; kernel smoothing; local linear regression; plug-in bandwidth; variable bandwidth.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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