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No BLUE among phylogenetic estimators.

P Joyce1

  • 1Department of Mathematics, Division of Statistics, University of Idaho, Moscow, ID 83844-1103, USA. joyce@uidaho.edu

Journal of Mathematical Biology
|December 22, 1999
PubMed
Summary

This study explores linear estimation in DNA polymorphism coalescent models, finding limitations for linear estimators. No uniformly best linear unbiased estimator (BLUE) exists for the mutation parameter under neutral evolution.

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Area of Science:

  • Statistics
  • Population Genetics
  • Bioinformatics

Background:

  • Multivariate analysis utilizes linear algebra for estimation theory.
  • Coalescent models are crucial for analyzing DNA polymorphism.
  • Classical estimation theory has limitations in biological contexts.

Purpose of the Study:

  • To develop a linear theory of estimation within coalescent models.
  • To investigate the extent of linear estimation applicability in DNA polymorphism analysis.
  • To identify limitations of linear estimators in this context.

Main Methods:

  • Exploration of a large class of coalescent models, including the neutral infinite sites model.
  • Application of multivariate statistical techniques.
  • Analysis of linear estimator performance compared to existing methods.

Main Results:

  • Identified limitations of linear estimators distinct from classical theory.
  • Proved the non-existence of a uniformly best linear unbiased estimator (BLUE) for the scaled mutation parameter under neutral evolution.
  • Demonstrated that no linear estimator uniformly outperforms the Watterson (1975) method based on segregating sites.

Conclusions:

  • If genealogical information aids evolution rate estimation, no optimal linear method exists.
  • If an optimal linear method exists, only segregating sites information is necessary.
  • The segregating-sites estimator is optimal for certain coalescent models.

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