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Estimation in Partially Linear Models and Numerical Comparisons.

Hua Liang1

  • 1Department of Biostatistics, St. Jude Children's Research Hospital, 332 North Lauderdale St., Memphis, TN 38105-2794.

Computational Statistics & Data Analysis
|February 23, 2010
PubMed
Summary
This summary is machine-generated.

Bandwidth selection for partially linear models is crucial. This study clarifies why undersmoothing is vital for backfitting methods and optimal bandwidths for profile-kernel methods, offering a general computation strategy.

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Area of Science:

  • Statistics
  • Non-parametric statistics

Background:

  • Partially linear models with local kernel regression are widely used.
  • Bandwidth selection is a challenging aspect of these models, with existing literature discussing undersmoothing and regular smoothing.

Purpose of the Study:

  • To address the strategy of bandwidth selection in partially linear models.
  • To review and compare profile-kernel based and backfitting methods.
  • To introduce and evaluate the penalized spline method.

Main Methods:

  • Review of profile-kernel based and backfitting methods for bandwidth selection.
  • Justification of undersmoothing necessity for backfitting.
  • Explanation of "optimal" bandwidth for profile-kernel methods.
  • Development of a general computation strategy for nonparametric function estimation.
  • Application of penalized spline method for partially linear models.

Main Results:

  • Simulation experiments demonstrate the numerical performance of penalized spline, profile, and backfitting methods.
  • A comparative analysis of the three methods is presented.
  • The study provides insights into the theoretical underpinnings of bandwidth selection strategies.

Conclusions:

  • Undersmoothing is essential for the backfitting method in partially linear models.
  • "Optimal" bandwidth selection is appropriate for profile-kernel based methods.
  • The penalized spline method offers a viable alternative for analyzing partially linear models, as supported by simulation and real-data analysis.