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Model Averaging Procedure for Partially Linear Single-index Models.

Yao Yu1, Sally W Thurston1, Russ Hauser2

  • 1Department of Biostatistics and Computational Biology, University of Rochester, NY 14642, U.S.A.

Journal of Statistical Planning and Inference
|May 20, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces new methods for model selection and averaging in partially linear single-index models. The proposed frequentist model average (FMA) approach improves accuracy in statistical analysis, outperforming traditional methods.

Keywords:
AICBICFocused information criterion (FIC)Frequentist model averaging (FMA)Profile least squares procedure

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Partially linear single-index models are widely used in various fields.
  • Model selection and averaging are crucial for robust statistical inference.
  • Existing methods may not be optimal for these complex models.

Purpose of the Study:

  • To develop and evaluate novel model selection and averaging procedures for partially linear single-index models.
  • To introduce the Focused Information Criterion (FIC) and Frequentist Model Average (FMA) estimators.
  • To assess the performance of the proposed methods against traditional approaches.

Main Methods:

  • Utilizing profile least squares for coefficient estimation.
  • Deriving the Focused Information Criterion (FIC) based on asymptotic distributions.
  • Formulating Frequentist Model Average (FMA) estimators.
  • Constructing confidence intervals for FMA and FIC estimators.

Main Results:

  • Asymptotic normality of submodel estimators is established.
  • Monte Carlo simulations demonstrate the superiority of FIC and FMA.
  • Proposed methods show improved coverage probability and mean squared error compared to AIC and BIC.
  • Application to a male fertility study reveals insights into sperm concentration factors.

Conclusions:

  • The proposed FIC and FMA methods offer a robust framework for partially linear single-index models.
  • These methods provide more accurate and reliable statistical inference.
  • The approach is effective in real-world applications, such as environmental health studies.