This paper develops a test for homogeneity in finite mixture models where the mixing proportions are known a priori (taken to be 0.5) and a common nuisance parameter is present. Statistical tests based on the notion of Projected Likelihood Contrasts (PLC) are considered. The PLC is a slight modification of the usual likelihood ratio statistic or the Wilk’s Λ and is similar in spirit to the Rao’...

In the Laguerre ensemble of N ×N hermitian matrices, it is of interest both theoretically and for applications to quantum transport problems to compute the variance of a linear statistic, denoted varN f , as N → ∞. Furthermore, this statistic often contains an additional parameter α for which the limit α → ∞ is most interesting and most difficult to compute numerically. We derive exact expressi...

Abstract: In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure. As an application, we provide an asymptotic power function for the corrected likelihood ratio statistic for testing the presence of spi...

In this paper, we develop a Neyman-type smooth test for the serial dependence of unobservable generalized errors. Our test is "nuisance parameter-free" in the sense that model parameter estimation uncertainty has no impact on the limit distribution of the test statistic.

When processing observational data, statistical testing is an essential instrument to hopefully render harmless incidental anomalies and disturbances in the measurements. A commonly used test statistic based on the general linear model is the generalized likelihood ratio test statistic. The standard formula given in the literature for this test statistic is not defined if the noise covariance m...

Most existing statistical methods developed for calling single nucleotide polymorphisms (SNPs) using next-generation sequencing (NGS) data are based on Bayesian frameworks, and there does not exist any SNP caller that produces p-values for calling SNPs in a frequentist framework. To fill in this gap, we develop a new method MAFsnp, a Multiple-sample based Accurate and Flexible algorithm for cal...

Consider a model parameterized by a scalar parameter of interest and a nuisance parameter vector. Inference about the parameter of interest may be based on the signed root of the likelihood ratio statistic R. The standard normal approximation to the conditional distribution of R typically has error of order O(n−1/2), where n is the sample size. There are several modifications for R, which reduc...

We describe an extension of the fixed-b approach introduced by Kiefer and Vogelsang (2005) to the empirical likelihood estimation framework. Under fixed-b asymptotics, the empirical likelihood ratio statistic evaluated at the true parameter converges to a nonstandard yet pivotal limiting distribution that can be approximated numerically. The impact of the bandwidth parameter and kernel choice i...

1. Abstract Asymptotic expansions of the distributions of parameter estimators in mean and covariance structures are derived. The parameters may be common to or specific in means and covariances of observable variables. The means are possibly structured by the common/specific parameters. First, the distributions of the parameter estimators standardized by the population asymptotic standard erro...