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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
Summary
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.
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.
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