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Small-sample confidence regions in exponential families.
1Department of Biostatistics, University of Rochester, New York 14642, USA. kolassa@bst.rochester.edu
Biometrics
|April 21, 2001
Summary
This study introduces a novel algorithm for creating small-sample conditional confidence regions in discrete generalized linear models. The method efficiently constructs these regions by inverting conditional hypothesis tests, improving statistical inference for complex models.
Area of Science:
- Statistics
- Computational Statistics
Background:
- Accurate confidence regions are crucial for parameter estimation in statistical models.
- Small-sample inference presents unique challenges, particularly for discrete regression models.
Purpose of the Study:
- To develop an algorithm for constructing small-sample conditional confidence regions for discrete regression models.
- To enhance the efficiency of confidence region computation within the generalized linear interactive model family.
Main Methods:
- The algorithm inverts conditional hypothesis tests to define confidence regions.
- It utilizes exact or approximate Monte Carlo methods for sample space enumeration.
- Conditional probabilities are computed and transformed using exponential tilting for parameter estimation.
Main Results:
- The proposed method provides a computationally efficient way to determine conditional confidence regions.
- It leverages properties of exponential families to reduce computational burden.
- The algorithm successfully constructs regions with a specified confidence level (1 - alpha).
Conclusions:
- The developed algorithm offers a robust approach for small-sample conditional inference in discrete regression.
- This method significantly reduces computational effort, making complex statistical analyses more accessible.
- The findings are applicable to various discrete regression models within the generalized linear interactive model family.