Geometry of the log-likelihood ratio statistic in misspecified models

Approximating the F distribution via a general version of the modified signed log-likelihood ratio statistic

A simple normal approximation for the cumulative distribution function of the F distribution is obtained via a general version of the modified signed log-likelihood ratio statistic. This approximation exhibits remarkable accuracy even when the degrees of freedom are small. Using the same methodology, but with a simpler set up, simple and accurate normal approximations to the cumulative distribu...

An Optimal Property of the Likelihood Ratio Statistic

Non-Nested Models and the Likelihood Ratio Statistic: A Comparison of Simulation and Bootstrap Based Tests

We consider an alternative use of simulation in the context of using the Likelihood-Ratio statistic to test non-nested models. To date simulation has been used to estimate the Kullback-Leibler measure of closeness between two densities, which in turn ’mean adjusts’ the Likelihood-Ratio statistic. Given that this adjustment is still based upon asymptotic arguments, an alternative procedure is to...

On the Asymptotic Performance of the Log Likelihood Ratio Statistic for the Mixture Model and Related Results I

The classical distribution theory of the log likelihood ratio test statistic does not hold for testing homogeneity (i.e., no mixture) against mixture alternatives. Asymptotic theory for this problem is developed. For some special cases, asymptotically locally minimax tests are also found. It is pointed out that the main problem is lack of identifiability of the usual parameterization even when ...

Mixture Likelihood Ratio Scan Statistic for Disease Outbreak Detection

Early detection of disease outbreaks is of paramount importance to implementing intervention strategies to mitigate the severity and duration of the outbreak. We build methodology that utilizes the characteristic profile of disease outbreaks to reduce the time to detection and false positive rate. We model daily counts through a Poisson distribution with additive background plus outbreak compon...