Image detection under low-light-level conditions is treated as a hypothesis-testing problem in which the observations are modeled as a shot-noise process. Since computing the likelihood ratio for shot-noise processes is not feasible, the use of a one-dimensional test statistic obtained by filtering and sampling the observations is proposed. The filter is chosen to maximize a generalized signal-...

We consider selection of nested and non-nested semiparametric models. Using profile likelihood we can define both a likelihood ratio statistic and an Akaike information for models with nuisance parameters. Asymptotic quadratic expansion of the log profile likelihood allows derivation of the asymptotic null distribution of the likelihood ratio statistic including the boundary cases, as well as u...

The main purpose of this paper is to introduce first a new family of empirical test statistics for testing a simple null hypothesis when the vector of parameters of interest are defined through a specific set of unbiased estimating functions. This family of test statistics is based on a distance between two probability vectors, with the first probability vector obtained by maximizing the empiri...

We study the problem of statistical inference of continuous-time diffusion processes, and develop methods for modeling threshold diffusion processes in particular. We derive the limiting properties of the quasi-likelihood estimator. We also propose a quasi-likelihood ratio test statistic for testing threshold diffusion process against linear alternative. We begin in Chapter 1 with an introducti...

Conditions for approximate frequentist validity of posterior credible sets based on the score statistic have been derived in the multiparameter case. These conditions can be helpful in supplementing similar conditions obtainable through the likelihood ratio statistic and the highest posterior density region. In the process, explicit expressions are given for the posterior quantiles of the score...

We consider the problem of testing for zero variance components in linear mixed models with correlated or heteroscedastic errors. In the case of independent and identically distributed errors, a valid test exists, which is based on the exact finite sample distribution of the restricted likelihood ratio test statistic under the null hypothesis. We propose to make use of a transformation to deriv...

For any generalized linear model, the Pearson goodness of fit statistic is the score test statistic for testing the current model against the saturated model. The relationship between the Pearson statistic and the residual deviance is therefore the relationship between the score test and the likelihood ratio test statistics, and this clarifies the role of the Pearson statistic in generalized li...