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Changjun Yu 《统计学通讯:理论与方法》2017,46(2):591-601
This paper investigates tail behavior of the randomly weighted sum ∑nk = 1θkXk and reaches an asymptotic formula, where Xk, 1 ? k ? n, are real-valued linearly wide quadrant-dependent (LWQD) random variables with a common heavy-tailed distribution, and θk, 1 ? k ? n, independent of Xk, 1 ? k ? n, are n non-negative random variables without any dependence assumptions. The LWQD structure includes the linearly negative quadrant-dependent structure, the negatively associated structure, and hence the independence structure. On the other hand, it also includes some positively dependent random variables and some other random variables. The obtained result coincides with the existing ones. 相似文献
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Nadezhda Gribkova 《统计学通讯:理论与方法》2017,46(23):11918-11932
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Assume that there are two types of insurance contracts in an insurance company, and the ith related claims are denoted by {Xij, j ? 1}, i = 1, 2. In this article, the asymptotic behaviors of precise large deviations for non random difference ∑n1(t)j = 1X1j ? ∑n2(t)j = 1X2j and random difference ∑N1(t)j = 1X1j ? ∑N2(t)j = 1X2j are investigated, and under several assumptions, some corresponding asymptotic formulas are obtained. 相似文献
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文章将利用已知的几种特殊的自然数的幂方和,研究其算法特征,进而给出并证明了自然数幂方和的一个巧妙猜想,希望这一猜想能给自然数的幂方求和寻求更简单的方法提供一些新思路. 相似文献
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C. Ming Wang 《统计学通讯:理论与方法》2013,42(14):1647-1659
The relationship between the mixed-model analysis and multivariate approach to a repeated measures design with multiple responses is presented. It is shown that by taking the trace of the appropriate submatrix of the hypothesis (error) sums of squares and crossproducts (SSCP) matrix obtained from the multivariate approach, one can get the hypothesis (error) SSCP matrix for the mixed-model analysis. Thus, when analyzing data from a multivariate repeated measures design, it is advantageous to use the multivariate approach because the result of the mixed-model analysis can also be obtained without additional computation. 相似文献
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The one-way random effects model with unequal variances and unequal sample sizes is considered. Estimation of the variances, variance of a single observation (total variance), and the standard error of the unweighted mean are considered. Precision of the Analysis of Variance and Unweighted Sums of Squares type of estimators and the Minimum Norm Quadratic Unbiased Estimators with a priori weights are examined. 相似文献
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S. P. Brooks 《Statistics and Computing》1998,8(3):267-274
Yu (1995) provides a novel convergence diagnostic for Markov chain Monte Carlo (MCMC) which provides a qualitative measure of mixing for Markov chains via a cusum path plot for univariate parameters of interest. The method is based upon the output of a single replication of an MCMC sampler and is therefore widely applicable and simple to use. One criticism of the method is that it is subjective in its interpretation, since it is based upon a graphical comparison of two cusum path plots. In this paper, we develop a quantitative measure of smoothness which we can associate with any given cusum path, and show how we can use this measure to obtain a quantitative measure of mixing. In particular, we derive the large sample distribution of this smoothness measure, so that objective inference is possible. In addition, we show how this quantitative measure may also be used to provide an estimate of the burn-in length for any given sampler. We discuss the utility of this quantitative approach, and highlight a problem which may occur if the chain is able to remain in any one state for some period of time. We provide a more general implementation of the method to overcome the problem in such cases. 相似文献
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Let {Xn,n≥1} be a sequence of independent identically distributed (i.i.d) random variables with a common distribution function F. When F belongs to the domain of partial attraction of a Semi-Stable law with index ,0<<2, we give complete solution to the results of R. Vasudeva and G. Divanji [Law of iterated logarithm for random subsequences, Statist. Probab. Lett. 12 (1991) 189–194], where they obtained Chover’s form of the law of iterated logarithm for random subsequences. Further, we extended the situation in obtaining almost sure limit points for random subsequences. 相似文献