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141.
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Summary This expository paper provides a framework for analysing de Finetti's representation theorem for exchangeable finitely additive
probabilities. Such an analysis is justified by reasoning of statistical nature, since it is shown that the abandonment of
the axiom of σ-additivity has some noteworthy consequences on the common interpretation of the Bayesian paradigm. The usual
(strong) fromulation of de Finetti's theorem is deduced from the finitely additive (weak) formulation, and it is used to solve
the problem of stating the existence of a stochastic process, with given finite-dimensional probability distributions, whose
sample paths are probability distributions. It is of importance, in particular, to specify prior distributions for nonparametric
inferential problems in a Bayesian setting.
Research partially supported by MPI (40% 1990, Gruppo Nazionale ?Modelli Probabilistici e Statistica Matematica?). 相似文献
143.
144.
Yanjiao Meng 《统计学通讯:理论与方法》2019,48(9):2206-2217
For negatively associated (NA) random variables, we obtain two general strong laws of large numbers (SLLN) in which the coefficient of sum and the weight are both general functions. As corollaries, we obtain Marcinkiewicz-type SLLN, the logarithmic SLLN and Marcinkiewicz SLLN for NA random variables. 相似文献
145.
We provide a comprehensive and critical review of Yates’ continuity correction for the normal approximation to the binomial distribution, in particular emphasizing its poor ability to approximate extreme tail probabilities. As an alternative method, we also review Cressie's finely tuned continuity correction. In addition, we demonstrate how Yates’ continuity correction is used to improve the coverage probability of binomial confidence limits, and propose new confidence limits by applying Cressie's continuity correction. These continuity correction methods are numerically compared and illustrated by data examples arising from industry and medicine. 相似文献
146.
The Craig-Sakamoto theorem establishes a sufficient and necessary condition for the independence of two quadratic forms in normal variates, fascinating many statisticians and mathematicians, who continuously seek for simple and better proofs of the theorem and its extensions. In this article, we present a simple proof of a unified theorem on the independence of linear and quadratic functions in general normal variates. 相似文献
147.
In this article, we develop a new Rosenthal Inequality for uniform random permutation sums of random variables with finite third moments and apply it to obtain a sharp non-uniform bound for the combinatorial central limit theorem using the Stein's method and the exchangeable pair techniques. The obtained bound is shown to be sharper than other existing bounds. 相似文献
148.
Abstract. Functional measures of skewness and kurtosis, called asymmetry and gradient asymmetry functions, are described for continuous univariate unimodal distributions. They are defined and interpreted directly in terms of the density function and its derivative. Asymmetry is defined by comparing distances from points of equal density to the mode. Gradient asymmetry is defined, in novel fashion, as asymmetry of an appropriate function of the density derivative. Properties and illustrations of asymmetry and gradient asymmetry functions are presented. Estimation of them is considered and illustrated with an example. Scalar summary skewness and kurtosis measures associated with asymmetry and gradient asymmetry functions are discussed. 相似文献
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