Suppose that we have the density ß›y;Sfi of a model with the null hypothesis of the form H 0;S = S 0 . Let L›Sfi be the log-likelihood function of the model and  S be the MLE of S. Wald test is based on the very intuitive idea that we are willing to accept the null hypothesis when  S is close to S 0 . The distance between  S and S 0 is the basis of constructing the test statistic. On the oth...

This study considers Rao test and Wald test for adaptive detection based on a diversely polarized antenna (DPA) in partially homogeneous environment. The theoretical expressions for the probability of false alarm and detection are derived, and constant false alarm rate (CFAR) behaviour is remarked on. Furthermore, the monotonicities of detection probability of the two detectors are proved, and ...

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wal...

Feed-forward multi-layer neural network models, such as back-propagation networks with one or more hidden layers, present special challenges when it is necessary to evaluate and rank the contribution of each input variable. A number of methods have been proposed, including the multivariate Wald test and sensitivity analysis. Neither of these methods produces a complete and satisfactory answer t...

Questions relevant to DSM-V alcohol use disorders (AUD) include whether dimensional measures provide more information than categorical diagnoses, whether to combine abuse and dependence criteria, and whether to add a new diagnostic criterion, binge drinking. Binary and dimensional models of three versions of AUD criteria were investigated: (1) dependence criteria; (2) abuse and dependence crite...

We derive three likelihood-based confidence intervals for the risk ratio of two proportion parameters using a double sampling scheme for misclassified binomial data. The risk ratio is also known as the relative risk. We obtain closed-form maximum likelihood estimators of the model parameters by maximizing the full-likelihood function. Moreover, we develop three confidence intervals: a naive Wal...

Motivated by the problem of testing tetrad constraints in factor analysis, we study the large-sample distribution of Wald statistics at parameter points at which the gradient of the tested constraint vanishes. When based on an asymptotically normal estimator, the Wald statistic converges to a rational function of a normal random vector. The rational function is determined by a homogeneous polyn...