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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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A Legacy of EM Algorithms.

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  • 1Departments of Computational Medicine, Human Genetics, and Statistics, University of California Los Angeles, Los Angeles, 90095-1766CA, USA.

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|May 19, 2023
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Summary
This summary is machine-generated.

The minorisation-maximisation (MM) principle offers a generalized framework for computational statistics, enhancing algorithms like expectation-maximisation (EM). This approach simplifies derivations and can lead to faster convergence, particularly in complex, high-dimensional data analysis.

Keywords:
EM algorithmMM algorithmlongitudinal data analysisvariance component model

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Area of Science:

  • Computational Statistics
  • Statistical Algorithms
  • Mathematical Optimization

Background:

  • Nan Laird's significant contributions to computational statistics, particularly the expectation-maximisation (EM) algorithm and longitudinal modeling.
  • The widespread citation and impact of Laird's work in statistical research.
  • The need for more generalized and efficient statistical algorithms.

Purpose of the Study:

  • To revisit the derivation of Laird's key algorithms using the minorisation-maximisation (MM) principle.
  • To demonstrate how the MM principle generalizes the EM principle.
  • To explore new algorithmic possibilities and improved convergence rates.

Main Methods:

  • Application of the minorisation-maximisation (MM) principle.
  • Generalization of the expectation-maximisation (EM) principle.
  • Construction of surrogate functions using mathematical inequalities.

Main Results:

  • The MM principle provides a unified and simplified derivation for existing algorithms.
  • The MM principle can yield novel algorithms with potentially faster convergence rates than classical methods.
  • The MM principle offers a flexible framework applicable beyond missing data problems.

Conclusions:

  • The MM principle is a powerful generalization of the EM principle in computational statistics.
  • MM algorithms offer advantages in efficiency and applicability, especially for high-dimensional data.
  • This framework enhances the understanding and development of statistical algorithms.