相关论文: Likelihood ratio tests and singularities

In this paper new test statistics are introduced and studied for the important problem of testing hypothesis that involves inequality constraint on proportions when the sample comes from independent binomial random variables: Wald type and…

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…

In this paper we consider some hypothesis tests within a family of Wishart distributions, where both the sample space and the parameter space are symmetric cones. For such testing problems, we first derive the joint density of the ordered…

The problem of curve registration appears in many different areas of applications ranging from neuroscience to road traffic modeling. In the present work, we propose a nonparametric testing framework in which we develop a generalized…

The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses…

We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…

The Chernoff bound is an important inequality relation in probability theory. The original version of the Chernoff bound is to give an exponential decreasing bound on the tail distribution of sums of independent random variables. Recent…

We show that external randomization may enforce the convergence of test statistics to their limiting distributions in particular cases. This results in a sharper inference. Our approach is based on a central limit theorem for weighted sums.…

Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…

Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in…

The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…

We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…

In this paper, we propose corrections to the likelihood ratio test and John's test for sphericity in large-dimensions. New formulas for the limiting parameters in the CLT for linear spectral statistics of sample covariance matrices with…

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Necessary conditions for the existence of non-central Wishart distributions are given. Our method relies on positivity properties of spherical polynomials on Euclidean Jordan Algebras and advances an approach by Peddada and Richards (1991),…

Motivated by multiple statistical hypothesis testing, we obtain the limit of likelihood ratio of large deviations for self-normalized random variables, specifically, the ratio of $P(\sqrt{n}(\bar X +d/n) \ge x_n V)$ to $P(\sqrt{n}\bar X \ge…

We investigate the problem of semi-parametric maximum likelihood under constraints on summary statistics. Such a procedure results in a discrete probability distribution that maximises the likelihood among all such distributions under the…

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio…

Let $\mathbf {x}_1,\ldots,\mathbf {x}_n$ be a random sample from a $p$-dimensional population distribution, where $p=p_n\to\infty$ and $\log p=o(n^{\beta})$ for some $0<\beta\leq1$, and let $L_n$ be the coherence of the sample correlation…