We consider the problem of testing of a Kronecker product structured variance covariance matrix against the unstructured variance covariance matrix in the context of multivariate repeated measures data. A likelihood ratio test statistic is developed for this purpose. However, the test statistic for this test cannot be expressed in a closed form. An algorithm, is suggested for the maximum likeli...

We focus on a class of non-standard problems involving non-parametric estimation of a monotone function that is characterized by n rate of convergence of the maximum likelihood estimator, non-Gaussian limit distributions and the non-existence of ffiffiffi n p -regular estimators. We have shown elsewhere that under a null hypothesis of the type w(z0) 1⁄4 h0 (w being the monotone function of inte...

Higgs searches at LEP were based on marginal signal expectations and small background uncertainties. In contrast, Higgs searches at the LHC are based on strong signal expectations and relatively large background uncertainties. Based on our experience with the LEP Higgs search, our group tried to move the tools we had developed at LEP to the LHC environment. In particular, our calculation of con...

Sequential Probability Ratio Test (SPRT) has been widely used to detect process anomalies. The purpose of this paper is to present a practical procedure on the basis of SPRT, which recognizes if the mean of a latent Gaussian process Yt significantly deviates from presumed value, via an observable signal resulting from Yt. An equation for estimating the unknown nuisance parameter of the process ...

In classical statistics the likelihood ratio statistic used in testing hypotheses about covariance matrices does not have a closed form distribution, but asymptotically under strong normality assumptions is a function of the 2-distribution. This distributional approximation totally fails if the normality assumption is not completely met. In this paper we will present multivariate robust testing...

Abstract This paper considers the parameter estimation problem of a first-order threshold autoregressive conditional heteroscedasticity model by using empirical likelihood method. We obtain ratio statistic based on estimating equation least squares and construct confidence region for parameters. Simulation studies indicate that method outperforms normal approximation-based in terms coverage pro...

This article deals with the problem of testing the hypothesis that q p-variate normal distributions are independent and that their covariance matrices are equal. The exact null distribution of the likelihood ratio statistic when q = 2 is obtained using inverse Mellin transform and the definition of Meijer’s G-function. Results for p = 2, 3, 4 and 5 are given in computable series forms.

An approximation of the large deviation type is derived for tests of one-dimensional hypotheses in a general regular parametric model, possibly with nuisance parameters. The test statistic is most conveniently represented as a modiied log likelihood ratio statistic, just as the r-statistic from Barndorr-Nielsen (1986). In fact, the statistic is identical to a version of r , except that a certai...