International Statistical Review

How to Choose a Working Model for Measuring the Statistical Evidence About a Regression Parameter

Jeffrey D. Blume

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Abstract

Consider using a likelihood ratio to measure the strength of statistical evidence for one hypothesis over another. Recent work has shown that when the model is correctly specified, the likelihood ratio is seldom misleading. But when the model is not, misleading evidence may be observed quite frequently. Here we consider how to choose a working regression model so that the statistical evidence is correctly represented as often as it would be under the true model. We argue that the criteria for choosing a working model should be how often it correctly represents the statistical evidence about the object of interest (regression coefficient in the true model). We see that misleading evidence about the object of interest is more likely to be observed when the working model is chosen according to other criteria (e.g., parsimony or predictive accuracy).

Article information

Source
Internat. Statist. Rev., Volume 73, Number 3 (2005), 351-363.

Dates
First available in Project Euclid: 5 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.isr/1133819159

Zentralblatt MATH identifier
1105.62003

Keywords
The law of likelihood Statistical evidence Misleading evidence Model selection

Citation

Blume, Jeffrey D. How to Choose a Working Model for Measuring the Statistical Evidence About a Regression Parameter. Internat. Statist. Rev. 73 (2005), no. 3, 351--363. https://projecteuclid.org/euclid.isr/1133819159


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