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??Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.     

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Solar cell is the basic component of satellite photovoltaic panels with complicated redundant system structure. Its reliability plays an important role in the system, and its performance shows a degradation trend over time. In this paper, study is conducted for the solar cell degradation modeling and reliability analysis based on practical testing results. Specifically, we illustrate an accelerated test for the attenuation ratio character test under different accumulative irradiation levels, focusing on the heteroscedasticity of the collected testing data. A heteroscedastic linear model is proposed, and the life distribution of the photovoltaic panel is obtained by using Fiducial method. A numerical example is shown for the purpose of illustration.     

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At present, in degradation tests, product failure is generally defined as degradation of performance below or above a specified critical value (that is called single point degradation). Although this definition is simple and practical, it is not reasonable enough and degradation failure of the product can not be completely described. In this paper, a single point degradation model is improved, and an interval degeneration model is proposed. We discuss the interval degradation model when the degradation path is liner, and obtain life distribution functions for all kinds of linear interval degradation model. Numerical integration and Monte Carlo simulation methods are used to analyze and compare the life distribution of the interval degradation model and the single point degradation model, and the relationship between the interval degradation and the single point degradation is revealed. Finally, an real data example is analysis to show that interval egradation is more reasonable and effective in practice.     

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本文综述混合效应模型参数估计方面的若干新进展. 平衡混合效应方差分析模型的协方差阵具有一定结构. 对这类模型, 文献[1]提出了参数估计的一种新方法, 称为谱分解法. 新方法的突出特点是, 能同时给出固定效应和方差分量的估计, 前者是线性的, 后者是二次的,且相互独立. 而后, 文献[2--9]证明了谱分解估计的进一步的统计性质, 同时给出了协方差阵对应的估计, 它不仅是正定阵, 而且可获得它的风险函数, 这些文献还研究了谱分解估计与方差分析估计, 极大似然估计, 限制极大似然估计以及最小范数二次无偏估计的关系. 本文综述这一方向的部分研究成果, 并提出一些待进一步研究的问题.     

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??Let {X_n;\,n\ge1} be a sequence of strictly stationary \rho-mixing random variables with zero mean and finite variance. Using the weak convergence theorem and probability inequalities of \rho-mixing sequence, under some proper conditions, we obtained general laws of precise asymptotics for partial sums of \rho-mixing sequence.     

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In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It\^{o} integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment. According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.     

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The heteroscedasticity is inevitable for the panel data modeling in economics. The two-stage estimation method is a better means to study the heteroscedasticity, in which the basis is to select only one independent variable for samples grouping, it can cause the information used is incomplete. In this paper, we propose to select several variables for grouping using variable selection method, then k-mean algorithm is used to cluster, so the samples classification can be achieved and the heteroscedasticity estimation can be obtained. The results of real example analysis show that the method presented in this paper has obvious advantages in effectiveness and feasibility.     

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??A new risk model is constructed, where the total number of claims satisfies the geometric first-order integer-valued autoregressive process. Moreover, we obtain the equation of the adjustment coefficient. We discuss the relationships among the dependence on the number of claims in each period, the adjustment coefficient, and ruin probability by numerical simulations. The results show that, with the increase of the dependence on the number of claims in each period, the adjustment coefficient decrease and ruin probability increase gradually.     

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??This paper is based on ``Pao-Lu Hsu's lecture' (2019/3/22) at Peking University and the subsequent expansion of his reports. It begins with some recollections benefited of the author from Professor Hsu, and ends with thanking to a group of professors at Peking University for their support and help over the past decades. The middle part is the theme of the talk. It gives first an overview of personal cross research. Then, from a challenge of computing, the author reports on the study looking for a larger class of complex matrices which have real spectrum. This was done mainly in the last year. It involves the fields of computation, probability, statistical mechanics and quantum mechanics Next, the paper introduces the latest development of algorithms, which is another illustration of the intersection between probability theory and computational mathematics. As the end, it also outlines the understanding of the cross study.     

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本文是对近十年来科学前沿热点问题之一的 全基因组关联研究(genome-wide association study, GWAS)的一个综述, 侧重于介绍其中所用到的统计分析方法, 讨论当前GWAS中存在的一些问题及挑战, 并就其发展前景作一个展望.     

Convergence for Sums of Asymptotically Almost Negatively Associated Random Variables

In this paper, by applying the moment inequality for asymptotically almost negatively associated (AANA, in short) random sequence and truncated method, the equivalent conditions of complete moment convergence of the maximum partial for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of{15},{16} and {17}, respectively.     

Complete Convergence for Weighted Sums of Arrays of Rowwise Asymptotically Almost Negative Associated Random Variables

Let be an array of rowwise asymptotically almost negative associated (AANA, in short) random variables. The complete convergence for weighted sums of arrays of rowwise AANA random variables is established under some general moment conditions. The result obtained in the paper generalizes and improves the corresponding one for negatively associated random variables.     

The Convergence of a Moving Average Process of AANA Random Variables

Based on the asymptotically almost negatively associated(AANA) random vari-ables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log(1+Y )] < ∞. As an application, Marcinkiewicz-Zygmund-type strong law of large numbers for this moving average process is presented in this paper.     

Equivalent Conditions of Complete qth Moment Convergence for Weighted Sums of Sequences of Negatively Orthant Dependent Random Variables

In this paper, the complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables are established. These results not only extend the corresponding results obtained by Li and Sp\v{a}taru\ucite{4}, Liang et al.\ucite{5}, Guo\ucite{6} and Gut\ucite{21} to sequences of negatively orthant dependent random variables, but also improve them.     

Strong convergence for sequences of asymptotically almost negatively associated random variables

In this article, the complete convergence for sequences of asymptotically almost negatively associated (AANA) random variables is studied. As applications, the Baum–Katz-type theorem, Hsu–Robbins-type theorem and Marcinkiewicz–Zygmund strong law of large numbers for sequences of AANA random variables are obtained.     

随机变量序列乘积和的矩完全收敛性

利用王岳宝等将乘积和转化为部分和的乘积之和的方法,研究了随机变量序列乘积和的矩完全收敛性,获得了乘积和矩完全收敛的充分条件.     

Complete moment convergence for arrays of rowwise NSD random variables

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.     

PA随机变量产生的移动平均过程的矩完全收敛性

设{ε_i:-∞i∞}是同分布正相协随机变量序列,{a_i:-∞i+∞}是绝对可和的常数列.在一定的条件下得到了移动平均过程(?)的矩完全收敛的精确渐近性.把有关负相协条件下的结果推广到正相协情形.     

Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables

In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.     

同分布ρ混合序列的矩完全收敛性

获得了同分布ρ混合序列的矩完全收敛性成立的充分必要性条件,推广和改进了已有的结果.