A ratio test

A Likelihood-Ratio Test of Monophyly

?Many phylogenetic analyses are inspired by or depend upon the monophyly of a group specified a priori. Also, many evolutionary problems for which phylogenies are useful do not require every detail of the phylogeny to be estimated correctly but depend upon the monophyly (or lack thereof) of a particular group. We propose a likelihood-ratio test that compares whether the best trees estimated wit...

A Mean Likelihood Ratio Speci cation Test

This paper considers the problem of speci cation testing in general parametric models and shows that for a wide class of models the hypothesis of correct speci cation is equivalent to a continuum of moment equalities. Using these moment equalities we construct a class of speci cation tests that have correct asymptotic size in general parametric models, including stationary time series models, a...

The mean–variance ratio test—A complement to the coefficient of variation test and the Sharpe ratio test

To circumvent the limitations of the tests for coefficients of variation and Sharpe ratios, we develop the mean-variance-ratio statistic to test the equality of the meanvariance ratios and prove that our proposed statistic is uniformly most powerful unbiased. In addition, we illustrate the applicability of our proposed test to compare the performances of stock indices.

1 Likelihood Ratio Test ( LRT

A New Approximation for the Null Distribution of the Likelihood Ratio Test Statistics for k Outliers in a Normal Sample

Usually when performing a statistical test or estimation procedure, we assume the data are all observations of i.i.d. random variables, often from a normal distribution. Sometimes, however, we notice in a sample one or more observations that stand out from the crowd. These observation(s) are commonly called outlier(s). Outlier tests are more formal procedures which have been developed for detec...