JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS)
Year:2004 | Volume:3 | Issue:1|Papers Count:4

In this paper we contribute to the general philosophical question as to whether empirical testing can ever prove a physical law. Problems that lead to this question arise under several contexts, and the matter has been addressed by the likes of Bayes and Laplace. After pointing out that a Bayesian approach is the proper way to address this problem, we show that the answer depends on what we start with. Namely, under certain prior assumptions, a finite amount of testing can lead to the conclusion of total trustworthiness, though such priors could be unrealistic. However, we do produce a new class of priors under which a finite amount of testing can lead to a high degree of trustworthiness, at a relatively fast pace. We use the scenario of software testing as a way to motivate and discuss our development.

Medical researchers may be interested in disease processes that are not directly observable. Imperfect diagnostic tests may be used repeatedly to monitor the condition of a patient in the absence of a gold standard. We consider parameter identifiability and estimability in a Markov model for alternating binary longitudinal responses that may be misclassified. Exactly two distinct sets of parameter values are shown to generate the distribution for the data in a common situation and we propose a restriction to distinguish the two. Even with the restriction, parameters may not be estimable. Issues of sampling and correct model specification are discussed.

We derive moment inequalities for the supremum of empirical processes of U-Statistic structure and give application to kernel type density estimation and estimation of the distribution function for functions of observations.

A conditional test based on quadratic form using type-2 censored sample for testing exponentiality against Weibull alternative is proposed. The simulated percentage points and powers are given. The proposed test performs well for identifying Weibull DFR alternative even for small sample. An example is also given.