When a reliability analysis, survival analysis, or discrete-event simulation input modeling analysis is performed, it is typically the case that a modeler collects data associated with some system under consideration. Although this raw data provides an initial insight into the stochastic elements of the system, often it is desirable to construct a model of the system which is tractable for math...

The authors consider a special case of inference in the presence of nuisance parameters. They show that when the orthogonalized score function is a function of a statistic S, no Fisher information for the interest parameter is lost by using the marginal distribution of S rather than the full distribution of the observations. Therefore, no information for the interest parameter is recovered by c...

When the goal is to estimate the parameter of some population (e.g., mean or variance), the usual procedure is to design a probability sample to provide a sample statistic. As an example, we might estimate the parameter ‘true average cost’ of an inventory system (population mean, ) with the statistic ‘average cost for 12 months’ (sample mean, x ); or we might estimate the proportion of taxpayer...

In this paper, the estimation of a scale parameter t under a new and bounded loss function, based on a reflection of the gamma density function, is discussed. The best scale-invariant estimator of tis obtained and the admissibility of all linear functions of the sufficient statistic, for estimating t in the absence of a nuisance parameter, is investigated

This paper establishes monotonicity of the chi-square test statistic. As the more efficient parameter estimator is plugged into the test statistic, the degrees of freedom of the resulting chi-square test statistic monotonically increase.

Under model correctness, highly accurate inference on a scalar interest parameter in the presence of a nuisance parameter can be achieved by several routes, among them considering the bootstrap distribution of the signed root likelihood ratio statistic. The context of model mis-specification is considered and inference based on a robust form of the signed root statistic is discussed in detail. ...

This paper provides the practitioner with a method of ascertaining when the concentration parameter in a simultaneous equations model is small. We provide some exact distribution theory for a proposed statistic and show that the statistic possesses the minimal desirable characteristics of a test statistic when used to test that the concentration parameter is zero. The discussion is then extende...