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Parametrically guided estimation in nonparametric varying coefficient models with quasi-likelihood.

Clemontina A Davenport1, Arnab Maity1, Yichao Wu1

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27695, U.S.A.

Journal of Nonparametric Statistics
|July 7, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a guided estimation procedure for nonparametric varying coefficient models, improving accuracy and offering a new bandwidth selection method. The guided estimator shows better performance than the unguided one in simulations and real data analysis.

Keywords:
generalized linear modelslocal polynomial smoothingnonparametric regressionparametrically guided estimationvarying coefficient model

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Standard linear regression models have limitations in capturing complex covariate effects.
  • Nonparametric varying coefficient models offer flexibility but can suffer from asymptotic bias.
  • Parametrically guided estimation is a known technique to mitigate bias in nonparametric settings.

Purpose of the Study:

  • To develop and evaluate a guided estimation procedure for nonparametric varying coefficient models.
  • To establish the asymptotic properties of the proposed guided estimators.
  • To introduce a novel method for bandwidth selection based on bias-variance tradeoff.

Main Methods:

  • Development of a parametrically guided estimation procedure tailored for nonparametric varying coefficient models.
  • Theoretical analysis to establish asymptotic properties of the guided estimators.
  • Simulation studies and real data analysis to compare guided and unguided estimators.
  • A proposed method for bandwidth selection optimizing the bias-variance tradeoff.

Main Results:

  • The guided estimation procedure effectively reduces asymptotic bias in nonparametric varying coefficient models.
  • Asymptotic properties of the guided estimators are theoretically established.
  • The proposed bandwidth selection method provides a practical approach for model tuning.
  • Empirical comparisons demonstrate superior performance of the guided estimator over the unguided estimator.

Conclusions:

  • The developed guided estimation procedure is a valuable enhancement for nonparametric varying coefficient models.
  • The method offers improved estimation accuracy and a robust approach to bandwidth selection.
  • The findings are validated through both simulation and real-world data applications, highlighting practical utility.