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This article revisits sequential estimation of the autoregressive parameter β in a first-order autoregressive (AR(1)) model and construction of a sequential confidence region for a parameter vector θ in a first-order threshold autoregressive (TAR(1)) model. To resolve a theoretical conjecture raised in Sriram (1986), we provide a comprehensive numerical study that strongly suggests that theregretin using a sequential estimator of β can be significantlynegativefor many heavy-tailed error distributions and even for normal errors. Secondly, to investigate yet another conjecture about the limiting distribution of a sequential pivotal quantity for θ in a TAR(1) model, we conduct an extensive numerical study that strongly suggests that the sequential confidence region has much better coverage probability than that of a fixed sample counterpart, regardless of whether the θ values are inside or on or near the boundary of the ergodic region of the series. These highlight the usefulness of sequential sampling methods in fitting linear and nonlinear time series models. [ABSTRACT FROM AUTHOR]

In this article we propose a new general index that measures relationships between multiple sets of random vectors. This index is based on Kullback-Leibler (KL) information, which measures linear or nonlinear dependence between multiple sets using joint and marginal densities of affine transformations of the random vectors. Estimates of the matrixes are obtained by maximizing the KL information and are shown to be consistent. The motivation for introducing such an index comes from morphological integration studies, a topic in biological science. As a special case of this index, we define an overall measure of association and two other measures for dimension reduction. The use of these measures is illustrated through real data analysis in morphometric studies and extensive simulations, and their performance is compared with that of approaches based on canonical correlation analysis. Extensions of the aforementioned measures to multiple groups are also discussed. In contrast to canonical correlation analysis, our general index not only provides an overall measure of association, but also determines nonlinear relationships, thereby making it useful in many other applications. [ABSTRACT FROM AUTHOR]

Considerable time and energy involved in complete counting of large, but pre-specified, batch of Ns items could be saved by using weights of items. This article considers the case when the underlying distribution of weights, and its mean and variance are unknown. The problem is then reduced to that of finding an estimator of the mean and an optimal (small) sample size based on which a number [Ncirc]n of items in the batch can be determined. Using a fixed-width interval criterion, Nickerson [Nickerson, D.M. Another look at counting by weighing. Commun. Statist. Simula. 1993, 22 (2), 323–343] derived an optimal sample size, but it depends on the unknown coefficient of variation. For this case, we propose a batch-type sequential sampling scheme which requires substantially fewer sampling operations and no prior knowledge of the coefficient of variation, but performs as well as Nickerson's and other available procedures in the literature. This shows that a little bit of sampling using substantially fewer sampling operations can significantly reduce the effort of complete counting. [ABSTRACT FROM AUTHOR]