The almost sure convergence rate of the estimator of optimized certainty equivalent risk measure under α-mixing sequences

Conditional value-at-risk (CVaR) model is a kind of financial risk measure that is extensively supported and accepted by international financial community. Its optimized form can be regarded as an optimized certainty equivalent (OCE) risk measurement. In this paper, we mainly discuss and analyze the strong laws of large numbers and the convergence rate of OCE's estimator under α-mixing sequences. The result shows that the almost sure convergence rate of CVaR estimator is given by the results of OCE estimator. Its convergence rate is inversely proportional to the square root of the sample size under certain conditions. Its effectiveness is verified by simulation experiments for two classical α-mixing sequences.     

Inferences on functions of Pareto parameters with application to income inequality measures

The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the Pareto distribution function are expressed in terms of parameters defining the Pareto distribution. Inference procedures based on the generalized variable method, the large sample method, and the Bayesian method for testing of, and constructing confidence interval for, these measures are discussed. The results of Monte Carlo study are used to compare the performance of the suggested inference procedures from a population characterized by a Pareto distribution.     

Assessing the performance of variational methods for mixed logistic regression models

We present a variational estimation method for the mixed logistic regression model. The method is based on a lower bound approximation of the logistic function [Jaakkola, J.S. and Jordan, M.I., 2000, Bayesian parameter estimation via variational methods. Statistics & Computing, 10, 25–37.]. Based on the approximation, an EM algorithm can be derived that results in a considerable simplification of the maximization problem in that it does not require the numerical evaluation of integrals over the random effects. We assess the performance of the variational method for the mixed logistic regression model in a simulation study and an empirical data example, and compare it to Laplace's method. The results indicate that the variational method is a viable choice for estimating the fixed effects of the mixed logistic regression model under the condition that the number of outcomes within each cluster is sufficiently high.     

四级样态:高校对接"四种形态"的"度"

高校是“立德树人”培养高素质人才的基地，始终坚持在党的领导下办好中国特色社会主义高校，需要在思想和行动上执行好“四种形态”。正确认识当前高校践行“四种形态”存在的“精细治理”“文化管理”“经验管束”“粗放管理”等“四级样态”，对于高校党组织更好推进“四种形态”在高校落地生根具有重要意义     

Utilizing Bayesian predictive power in clinical trial design

The Bayesian paradigm provides an ideal platform to update uncertainties and carry them over into the future in the presence of data. Bayesian predictive power (BPP) reflects our belief in the eventual success of a clinical trial to meet its goals. In this paper we derive mathematical expressions for the most common types of outcomes, to make the BPP accessible to practitioners, facilitate fast computations in adaptive trial design simulations that use interim futility monitoring, and propose an organized BPP-based phase II-to-phase III design framework.     

Empirical Bayes estimation in continuous one-parameter exponential families under associated samples

In this paper, we study the empirical Bayes (EB) estimation in continuous one-parameter exponential families under negatively associated (NA) samples and positively associated (PA) samples. Under certain regularity conditions, it is shown that the convergence rates of proposed EB estimators under NA or PA samples are the same as those of EB estimators under independent observations, which significantly improve the existing results in EB estimation under associated samples.     

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.     

Complete convergence and the strong laws of large numbers for pairwise NQD random variables

The authors study the strong convergence for sequences of pairwise negatively quadrant dependent (NQD) random variables under some wide conditions, and present some new theorems on the complete convergence and the strong laws of large numbers. The obtained results extend and improve some theorems in existing literature.     

Rare and clustered population estimation using the adaptive cluster sampling with some robust measures

The use of robust measures helps to increase the precision of the estimators, especially for the estimation of extremely skewed distributions. In this article, a generalized ratio estimator is proposed by using some robust measures with single auxiliary variable under the adaptive cluster sampling (ACS) design. We have incorporated tri-mean (TM), mid-range (MR) and Hodges-Lehman (HL) of the auxiliary variable as robust measures together with some conventional measures. The expressions of bias and mean square error (MSE) of the proposed generalized ratio estimator are derived. Two types of numerical study have been conducted using artificial clustered population and real data application to examine the performance of the proposed estimator over the usual mean per unit estimator under simple random sampling (SRS). Related results of the simulation study show that the proposed estimators provide better estimation results on both real and artificial population over the competing estimators.     

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.