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Related Experiment Videos

On L convergence of Neumann series approximation in missing data problems.

Hua Yun Chen1

  • 1Division of Epidemiology & Biostatistics, School of Public Health, University of Illinois at Chicago, 1603 West Taylor Street, Chicago, IL 60612.

Statistics & Probability Letters
|April 13, 2010
PubMed
Summary

This study demonstrates L(∞) convergence for Neumann series approximations of the nonparametric information operator inverse. This advance is crucial for analyzing doubly robust and semiparametric efficient estimators in complex missing data scenarios.

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Area of Science:

  • Statistics
  • Statistical Inference
  • Missing Data Analysis

Background:

  • The inverse of the nonparametric information operator is essential for developing doubly robust and semiparametric efficient estimators in missing data problems.
  • Nonmonotone missing data patterns lack a closed-form expression for this inverse, necessitating approximations like the Neumann series.
  • Current Neumann series approximations are limited to L(2) convergence, insufficient for establishing estimator properties.

Purpose of the Study:

  • To establish L(∞) convergence for Neumann series approximations of the nonparametric information operator inverse and efficient scores.
  • To enable the study of asymptotic properties for estimators in challenging missing data situations.

Main Methods:

  • Demonstrating L(∞) convergence of Neumann series approximations under simple conditions.
  • Applying these approximations to the inverse of the nonparametric information operator and efficient scores.

Main Results:

  • Achieved L(∞) convergence for Neumann series approximations, a significant improvement over existing L(2) convergence.
  • Established conditions for this improved convergence in the context of missing data.

Conclusions:

  • The findings pave the way for rigorous analysis of doubly robust and locally semiparametric efficient estimators.
  • This work addresses critical theoretical gaps in handling nonmonotone missing data patterns.