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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Partially Linear Models with Missing Response Variables and Error-prone Covariates.

Hua Liang1, Suojin Wang, Raymond J Carroll

  • 1Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, New York 14642, U.S.A.

Biometrika
|March 9, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces new statistical methods for analyzing data with missing outcomes and measurement errors in covariates, addressing complex missing not at random structures. The methods provide reliable estimation and confidence intervals for partially linear models.

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Partially linear models are widely used in various fields.
  • Handling missing data and measurement errors simultaneously is challenging.
  • The missingness mechanism is often 'missing not at random' (MNAR), complicating standard approaches.

Purpose of the Study:

  • To develop robust semiparametric estimators for partially linear models with missing outcomes and covariate errors.
  • To estimate the parameter of interest (beta) and the population mean E(Y) under complex missingness.
  • To construct asymptotically valid confidence regions for beta.

Main Methods:

  • Proposed a class of semiparametric estimators accounting for both missing outcomes and covariate errors.
  • Developed an empirical-likelihood-based statistic for confidence region construction.
  • Assumed missingness probability depends on observed and unobserved data (MNAR).

Main Results:

  • The proposed estimators for beta and E(Y) are consistent and asymptotically normal.
  • The empirical-likelihood statistic follows a chi-squared distribution asymptotically.
  • Methods were validated using an AIDS clinical trial dataset and simulation studies.

Conclusions:

  • The developed statistical methods effectively handle partially linear models with complex missing data and measurement error.
  • The estimators provide reliable inference for key parameters.
  • The approach is applicable to real-world data, as demonstrated in an AIDS clinical trial.