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Reducing Bias for Maximum Approximate Conditional Likelihood Estimator with General Missing Data Mechanism.

Jiwei Zhao1

  • 1Department of Biostatistics, State University of New York at Buffalo, Buffalo, NY, USA.

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|September 26, 2019
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Summary
This summary is machine-generated.

This study introduces a flexible missing data analysis method applicable to all missing data scenarios. Resampling techniques like Jackknife and Bootstrap are used to reduce estimation bias and improve statistical inference for incomplete datasets.

Keywords:
Missing data mechanismapproximate conditional likelihoodbiashigher order asymptotic expansionresampling

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Area of Science:

  • Statistics
  • Data Science
  • Biostatistics

Background:

  • Missing data analysis relies on unverifiable assumptions about the missing data mechanism.
  • Existing methods often require stringent assumptions (e.g., missing completely at random, missing at random, missing not at random).
  • A more flexible approach is needed to handle various missing data scenarios robustly.

Purpose of the Study:

  • To develop a generally applicable missing data mechanism that encompasses all missing data scenarios.
  • To introduce conditional likelihood and its approximation for parameter estimation under this general mechanism.
  • To propose resampling techniques (Jackknife, Bootstrap) to mitigate estimation bias caused by approximate likelihoods.

Main Methods:

  • Utilized a generalized missing data mechanism covering missing completely at random, missing at random, and missing not at random.
  • Introduced conditional likelihood and an approximate version for parameter estimation.
  • Applied Jackknife and Bootstrap resampling methods to reduce estimation bias.
  • Analyzed asymptotic biases up to O(n^-1) and derived mean squared error results.

Main Results:

  • The proposed method offers a flexible framework for missing data analysis.
  • Resampling techniques effectively reduce estimation bias associated with approximate conditional likelihoods.
  • Asymptotic bias and mean squared error analyses provide insights into estimation accuracy.
  • Simulations demonstrate the method's performance across various scenarios.

Conclusions:

  • The developed method provides a robust approach to missing data analysis under a general missing data mechanism.
  • Jackknife and Bootstrap resampling are effective in improving the accuracy of statistical inference with incomplete data.
  • The approach is validated through simulations and applied to a real-world prostate cancer dataset.