相关论文: The Two-Way Likelihood Ratio (G) Test and Comparis…

We consider whether the asymptotic distributions for the log-likelihood ratio test statistic are expected to be Gaussian or chi-squared. Two straightforward examples provide insight on the difference.

We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…

Two modifications of the chi square test for comparing usual(unweighted) and weighted histograms and two weighted histograms are proposed. Numerical examples illustrate an application of the tests for the histograms with different…

Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence…

We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…

The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the…

Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…

For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…

In this paper, we use the method of modified signed log-likelihood ratio test for the problem of testing the equality of correlation coefficients in two independent bivariate normal distributions. We compare this method with two other…

In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…

Histograms with weighted entries are used to estimate probability density functions. Computer simulation is the main application of this type of histograms. A review on chi-square tests for comparing weighted histograms is presented in this…

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics…

Wilk's theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the…

Recently Liu and Wang derived the likelihood ratio test (LRT) statistic and its asymptotic distribution for testing equality of two multinomial distributions vs. the alternative that the second distribution is larger in terms of increasing…

We present a new way of testing ordered hypotheses against all alternatives which overpowers the classical approach both in simplicity and statistical power. Our new method tests the constrained likelihood ratio statistic against the…

In this paper, we use the empirical likelihood method to construct the confidence regions for the difference between the parameters of a two-phases nonlinear model with random design. We show that the empirical likelihood ratio has an…

In this paper new families of test statistics are introduced and studied for the problem of comparing two treatments in terms of the likelihood ratio order. The considered families are based on phi-divergence measures and arise as natural…

Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how…

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…

Composite likelihood inference has gained much popularity thanks to its computational manageability and its theoretical properties. Unfortunately, performing composite likelihood ratio tests is inconvenient because of their awkward…