Confidence Bounds for Multiplicative Comparisons

Statements that are inherently multiplicative have historically been justified using ratios of random variables. Although recent work on ratios has extended the classical theory to produce confidence bounds conditioned on a positive denominator, this current article offers a novel perspective that e...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2011-09, Vol.40 (17), p.3049-3054
Main Authors: Ennis, John M., Ennis, Daniel M.
Format: Article
Language:English
Subjects:
Conditioning
Confidence
Confidence interval
Confidence intervals
Estimation
Exact sciences and technology
General topics
Global analysis, analysis on manifolds
Mathematics
Multiplicative comparison
Multiplicative statement
Nonparametric inference
Parametric inference
Primary 62F25
Probability and statistics
Random variables
Ratio statement
Ratios
Ratios of normal random variable
Sciences and techniques of general use
Secondary 62F03
Statistics
Studies
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:Statements that are inherently multiplicative have historically been justified using ratios of random variables. Although recent work on ratios has extended the classical theory to produce confidence bounds conditioned on a positive denominator, this current article offers a novel perspective that eliminates the need for such a condition. Although seemingly trivial, this new perspective leads to improved lower confidence bounds to support multiplicative statements. This perspective is also more satisfying as it allows comparisons that are inherently multiplicative in nature to be properly analyzed as such.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610921003646398