# Signal Detection and Model Selection

## Abstract

Signal detection is a basic statistical problem in various fields including engineering, econometrics and psychometrics. It is performed by statistical testing or model selection, but we cannot apply conventional statistical theory to it. The reason is that the signal model, a statistical model for signal detection, has an irregularity, called non-identifiability. Because of this non-identifiability problem, the signal model needs to be shrunk in its geometrical representation. After drawing it, we prove there is an asymptotic property of the likelihood ratio statistics for the model, which is indicated by the geometrical representation. Then, on the basis of this asymptotic property, we introduce a criterion for model selection considering non-identifiability that is a reevaluated Akaike information criterion (AIC). We check the validity of the reevaluated AIC through simulation studies and real data analysis using a factor analysis model, which can be regarded as a kind of signal model.

## Keywords

Factor analysis Information criterion Likelihood ratio Locally conic parameterization Non-identifiability## References

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