Moderate Deviations for Bayes Posteriors

Let ( X_k ) k be a sequence of i.i.d. random variables taking values in a set , and consider the problem of estimating the law of X₁ in a Bayesian framework. We prove, under mild conditions on the prior, that the sequence of posterior distributions satisfies a moderate deviation principle.     

A Comparative Study of Model-based Tests of Independence for Ordinal Data Using the Bootstrap

When analyzing categorical data using loglinear models in sparse contingency tables, asymptotic results may fail. In this paper the empirical properties of three commonly used asymptotic tests of independence, based on the uniform association model for ordinal data, are investigated by means of Monte Carlo simulation. Five different bootstrapped tests of independence are presented and compared to the asymptotic tests. The comparisons are made with respect to both size and power properties of the tests. Results indicate that the asymptotic tests have poor size control. The test based on the estimated association parameter is severely conservative and the two chi-squared tests (Pearson, likelihood-ratio) are both liberal. The bootstrap tests that either use a parametric assumption or are based on non-pivotal test statistics do not perform better than the asymptotic tests in all situations. The bootstrap tests that are based on approximately pivotal statistics provide both adjustment of size and enhancement of power. These tests are therefore recommended for use in situations similar to those included in the simulation study.     

Precise large deviations for the difference of two sums of END random variables with heavy tails

Assume that there are two types of insurance contracts in an insurance company, and the ith related claims are denoted by {X_ij, j ? 1}, i = 1, 2. In this article, the asymptotic behaviors of precise large deviations for non random difference ∑^n₁(t)_{j = 1}X_1j ? ∑^n₂(t)_{j = 1}X_2j and random difference ∑^N₁(t)_{j = 1}X_1j ? ∑^N₂(t)_{j = 1}X_2j are investigated, and under several assumptions, some corresponding asymptotic formulas are obtained.     

Hypothesis Testing in a Rayleigh Diffusion Model

Applying the large and moderate deviations for the log-likelihood ratio of the Rayleigh diffusion model, we give the negative regions in testing Rayleigh diffusion model and obtain the decay rates of the error probabilities.     

On An Intriguing Distributional Identity

For a continuous random variable X with support equal to (a, b), with c.d.f. F, and g: Ω₁ → Ω₂ a continuous, strictly increasing function, such that Ω₁∩Ω₂?(a, b), but otherwise arbitrary, we establish that the random variables F(X) ? F(g(X)) and F(g^{? 1}(X)) ? F(X) have the same distribution. Further developments, accompanied by illustrations and observations, address as well the equidistribution identity U ? ψ(U) = ^dψ^{? 1}(U) ? U for U ～ U(0, 1), where ψ is a continuous, strictly increasing and onto function, but otherwise arbitrary. Finally, we expand on applications with connections to variance reduction techniques, the discrepancy between distributions, and a risk identity in predictive density estimation.     

Elementary renewal theorems for widely dependent random variables with applications to precise large deviations

Abstract

On the basis of Wang and Cheng (J. Math. Anal. Appl. 384 (2011) 597–606), this paper further investigates elementary renewal theorems for counting processes generated by random walks with widely orthant dependent increments. The obtained results improve the corresponding ones of the above-mentioned paper mainly in the sense of weakening the moment conditions on the positive parts of the increments. Meanwhile, a revised version of strong law of large numbers for random walks with widely orthant dependent increments is established, which improves Theorem 1.4 of Wang and Cheng (2011 Wang, Y., and D. Cheng. 2011. Basic renewal theorems for a random walk with widely dependent increments and their applications. Journal of Mathematical Analysis and Applications 384 (2):597–606. doi:10.1016/j.jmaa.2011.06.010.[Crossref], [Web of Science ®] , [Google Scholar]) by enlarging the regions of dominating coefficients. Finally, by using the above results, some precise large deviation results for a nonstandard renewal risk model are established, in which the innovations are widely orthant dependent random variables with common heavy tails, and the inter-arrival times are also widely orthant dependent.     

税收筹划税法规制的适度性

税收筹划中各方主体复杂利益的并存、冲突和变易,集中体现为国家财政权与国民财产权的对立和协调,并往往导致税收筹划税法规制中的法律"失度,"进而激发税法制度及其运行由"失度"走向"适度"的变革需求。从总体上看,税法对税收筹划的规制呈现"失度-适度"的二元化状态;从税法理论上分析,这一规制状态根源于"个人营利性"与"社会公共性"的基本矛盾。国家追求税法对税收筹划规制的适度性,就是要平衡协调各方利益主体之间的复杂利益关系,尽量缓解和消除这一基本矛盾,以期实现税法对国家财政权和国民财产权的均衡保护。惟其如此,才能构建起新的税收筹划规制分析模式,方才推动中国税收筹划规制制度不断创新。     

关于含参变量无穷积分的绝对一致收敛的注记

本文从一个反例 ,证明了即使∫∞af(x ,t)dt绝对收敛且一致收敛 ,但不能推出∫∞a |f(x ,t) |dt一致收敛。     

Lower bound of average centered L2-discrepancy for U-type designs

Uniform designs are widely used in various scientific investigations and industrial applications. By considering all possible level permutation of the factors, a connection between average centered L₂-discrepancy and generalized wordlength pattern for asymmetrical fractional factorial designs is derived. Moreover, we present new lower bounds to the average centered L₂-discrepancy for symmetrical and asymmetrical U-type designs. For illustration of the theoretical results, the lower bounds for symmetrical and asymmetrical U-type designs are tabulated, and numerical results indicate that our lower bounds behave well and can be recommended for use in practice.     

适度普惠型社会福利法律制度的构建

社会福利法律制度是对一个国家一定时期所有关于社会福利的法律和制度的总称。在传统社会福利制度下,我国社会福利法律制度存在一些缺陷:缺乏体系性、普遍性、组织性和监督性。我国在发展适度普惠型社会福利制度过程中,要构建发展性、正当性、需要满足型社会福利法律制度,形成在《社会福利法》统领下单项法和专项法组合在一起的综合性法律体系。