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A Class of Improved Parametrically Guided Nonparametric Regression Estimators

Author

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  • Carlos Martins-Filho
  • Santosh Mishra
  • Aman Ullah

Abstract

In this article we define a class of estimators for a nonparametric regression model with the aim of reducing bias. The estimators in the class are obtained via a simple two-stage procedure. In the first stage, a potentially misspecified parametric model is estimated and in the second stage the parametric estimate is used to guide the derivation of a final semiparametric estimator. Mathematically, the proposed estimators can be thought as the minimization of a suitably defined Cressie-Read discrepancy that can be shown to produce conventional nonparametric estimators, such as the local polynomial estimator, as well as existing two-stage multiplicative estimators, such as that proposed by Glad (1998). We show that under fairly mild conditions the estimators in the proposed class are [image omitted] asymptotically normal and explore their finite sample (simulation) behavior.

Suggested Citation

  • Carlos Martins-Filho & Santosh Mishra & Aman Ullah, 2008. "A Class of Improved Parametrically Guided Nonparametric Regression Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 542-573.
    • Handle: RePEc:taf:emetrv:v:27:y:2008:i:4-6:p:542-573
    DOI: 10.1080/07474930801960444
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    Citations

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    Cited by:

    1. Lee, Tae-Hwy & Tu, Yundong & Ullah, Aman, 2014. "Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting," Journal of Econometrics, Elsevier, vol. 182(1), pages 196-210.
    2. Yan Li & Liangjun Su & Yuewu Xu, 2015. "A Combined Approach to the Inference of Conditional Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-220, April.
    3. T. Senga Kiessé & M. Rivoire, 2011. "Discrete semiparametric regression models with associated kernel and applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 927-941.
    4. Gao, Jiti, 2012. "Identification, Estimation and Specification in a Class of Semi-Linear Time Series Models," MPRA Paper 39256, University Library of Munich, Germany, revised 14 May 2012.
    5. Pablo Guerróon‐Quintana & Molin Zhong, 2023. "Macroeconomic forecasting in times of crises," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 295-320, April.
    6. Talamakrouni, Majda & El Ghouch, Anouar & Van Keilegom, Ingrid, 2012. "Guided censored regression," LIDAM Discussion Papers ISBA 2012023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Li, Shuo & Tu, Yundong, 2016. "n-consistent density estimation in semiparametric regression models," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 91-109.
    8. Clemontina A. Davenport & Arnab Maity & Yichao Wu, 2015. "Parametrically guided estimation in nonparametric varying coefficient models with quasi-likelihood," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 195-213, June.
    9. Dungey, Mardi & Long, Xiangdong & Ullah, Aman & Wang, Yun, 2014. "A semiparametric conditional duration model," Economics Letters, Elsevier, vol. 124(3), pages 362-366.
    10. Majda Talamakrouni & Anouar El Ghouch & Ingrid Van Keilegom, 2015. "Guided Censored Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 214-233, March.
    11. Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    12. Jiti Gao, 2012. "Identification, Estimation and Specification in a Class of Semiparametic Time Series Models," Monash Econometrics and Business Statistics Working Papers 6/12, Monash University, Department of Econometrics and Business Statistics.
    13. George Athanasopoulos & Minfeng Deng & Gang Li & Haiyan Song, 2013. "Domestic and outbound tourism demand in Australia: a System-of-Equations Approach," Monash Econometrics and Business Statistics Working Papers 6/13, Monash University, Department of Econometrics and Business Statistics.
    14. Talamakrouni, Majda & Van Keilegom, Ingrid & El Ghouch, Anouar, 2016. "Parametrically guided nonparametric density and hazard estimation with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 308-323.

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