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Natural selection influences the frequencies of particular alleles and phenotypes within populations in several different ways. Primarily, natural selection can be directional, stabilizing, or disruptive. Directional selection favors one extreme trait and shifts the population towards that phenotype while selecting against individuals displaying alternate traits. Stabilizing selection favors an intermediate trait with a narrow range of variation. Deviation from the optimal phenotype towards an...
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Variable Selection in Kernel Regression Using Measurement Error Selection Likelihoods.

Kyle R White1, Leonard A Stefanski1, Yichao Wu1

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

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|April 10, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces the Measurement Error Kernel Regression Operator (MEKRO), a new nonparametric estimator for measurement error models. MEKRO offers shrinkage and selection properties, improving upon existing kernel regression techniques.

Keywords:
LASSONadaraya-Watsonbandwidth selectionfeature selectionnonparametric regressionsolution path

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Measurement error models are prevalent in various scientific fields.
  • Traditional kernel estimators may not adequately handle measurement error, leading to biased results.
  • Existing methods for addressing measurement error in nonparametric regression have limitations.

Purpose of the Study:

  • To develop a novel nonparametric shrinkage and selection estimator for measurement error models.
  • To introduce the Measurement Error Kernel Regression Operator (MEKRO) as an advancement over standard kernel estimators.
  • To provide a robust method for estimating kernel bandwidths in the presence of measurement error.

Main Methods:

  • The study utilizes a measurement error selection likelihood approach.
  • The proposed Measurement Error Kernel Regression Operator (MEKRO) optimizes a likelihood function for bandwidth estimation.
  • A tuning parameter controls shrinkage and selection, with small-sample-corrected AIC used for selection.

Main Results:

  • MEKRO demonstrates solution paths similar to LASSO and COSSO, enabling simultaneous shrinkage and selection.
  • Theoretical large-sample properties of MEKRO are established.
  • Monte Carlo experiments and real-world data applications explore the small-sample performance of MEKRO.

Conclusions:

  • MEKRO provides a powerful new tool for nonparametric regression with measurement error.
  • The estimator offers data-driven bandwidth selection and variable selection capabilities.
  • MEKRO shows promise for improving statistical inference in models with latent errors.