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Optimal Stein-type goodness-of-fit tests for count data.

Christian H Weiß1, Pedro Puig2,3, Boris Aleksandrov1

  • 1Department of Mathematics and Statistics, Helmut Schmidt University, Hamburg, Germany.

Biometrical Journal. Biometrische Zeitschrift
|September 27, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces optimal Stein-type goodness-of-fit tests for count data. These tests enhance statistical analysis by optimizing weight functions for improved performance in Poisson and binomial distributions.

Keywords:
Stein-Chen identityasymptotic power analysisbinomial Stein identitycount datagoodness-of-fit test

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Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Count data analysis commonly uses Poisson and binomial distributions.
  • Goodness-of-fit (GoF) tests assess how well data fit a distribution.
  • Stein identities offer a framework for developing GoF tests.

Purpose of the Study:

  • To derive asymptotic properties of Poisson and binomial Stein-type GoF statistics.
  • To enable computation of asymptotic power for arbitrary alternatives.
  • To facilitate the implementation of optimal Stein tests for count data.

Main Methods:

  • Utilized Stein identities to define goodness-of-fit tests.
  • Derived asymptotic distributions for Stein-type statistics under Poisson and binomial models.
  • Considered weighted means based on user-selected weight functions.
  • Investigated negative-binomial distributions briefly.

Main Results:

  • Developed a method for computing asymptotic power of Stein-type GoF tests.
  • Enabled efficient implementation of optimal Stein tests.
  • Demonstrated the performance of optimal tests through simulations and medical data analysis.

Conclusions:

  • Optimal Stein-type GoF tests provide a powerful tool for analyzing count data.
  • The derived asymptotic properties allow for tailored test selection based on alternative scenarios.
  • The methodology is applicable to various count distributions, including Poisson, binomial, and negative-binomial.