Focused estimation for noisy and small data sets: a Bayesian minimum expected loss estimator approach

Central to many inferential situations is the estimation of rational functions of parameters. The mainstream in statistics and econometrics estimates these quantities based on the plug‐in approach without consideration of the main objective of the inferential situation. We propose the Bayesian Minimum Expected Loss (MELO) approach focusing explicitly on the function of interest, and calculating its frequentist variability. Asymptotic properties of the MELO estimator are similar to the plug‐in approach. Nevertheless, simulation exercises show that our proposal is better in situations characterised by small sample sizes and/or noisy data sets. In addition, we observe in the applications that our approach gives lower standard errors than frequently used alternatives when data sets are not very informative.     

Conditional design of the CUSUM median chart for the process position when process parameters are unknown

In practice, different practitioners will use different Phase I samples to estimate the process parameters, which will lead to different Phase II control chart's performance. Researches refer to this variability as between-practitioners-variability of control charts. Since between-practitioners-variability is important in the design of the CUSUM median chart with estimated process parameters, the standard deviation of average run length (SDARL) will be used to study its properties. It is shown that the CUSUM median chart requires a larger amount of Phase I samples to sufficiently reduce the variation in the in-control ARL of the CUSUM median chart. Considering the limitation of the amount of the Phase I samples, a bootstrap approach is also used here to adjust the control limits of the CUSUM median chart. Comparisons are made for the CUSUM and Shewhart median charts with estimated parameters when using the adjusted- and unadjusted control limits and some conclusions are made.     

Comparison of efficiencies of some symmetry tests around an unknown centre

In this paper, some recent and classical tests of symmetry are modified for the case of an unknown centre. The unknown centre is estimated with its α-trimmed mean estimator. The asymptotic behaviour of the new tests is explored. The local approximate Bahadur efficiency is used to compare the tests to each other as well as to some other tests.     

The use of simple reparameterizations to improve the efficiency of Markov chain Monte Carlo estimation for multilevel models with applications to discrete time survival models

Summary.  We consider the application of Markov chain Monte Carlo (MCMC) estimation methods to random-effects models and in particular the family of discrete time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete time survival analysis involves expanding the data set so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However, the data expansion results in very large data sets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterization techniques can be used and assess their performance.     

信贷风险管理的区间数参数模型及其应用

针对商业银行的风险与收益的不确定性,建立了基于区间数的参数规划模型。银行通过选择风险损失参数α,应用该模型即可确定出在风险/收益均衡状态下,不同风险信贷项目的最优组合投放权重,获得既定风险下的最大收益。最后,给出的算例表明了该方法对商业银行的信贷风险管理具有较强的应用价值。     

具有时滞的非线性系统的k-全局稳定性

研究了具有时滞的非线性系统的稳定性问题，利用不等式分析技巧和常数变易法，给出了具有时滞的非线性系统的ｋ－全局指数稳定性的充分条件。并举例说明了所得结论的优越性     

项目特征函数的导出及其特征研究

通过一个维度一个雏度地刻划,然后将刻划结果联合起来的方式,推导出了项目反应特征函数,并用数学分析的方法,探讨了项目反应理论框架中的项目难度参数和区分度参数的本质及其与经典真分数理论中的项目难度参数和区分度参数的异同,并指出了项目反应理论在应用中的一些误解和误用.     

基于利率平价关系的汇率模型

建立了基于利率平价关系的汇率模型，导出了汇率期权的定价公式，研究了该模型的检验问题和模型参数的估计问题，结果表明，在原测度下，该模型的统计推断问题难度很大，使用通常的时间序列分析方法不能得出令人满意的结论；而在等价鞅测度下讨论该模型的统计推断问题，大大降低了研究的难度．     

Performance of some new Liu parameters for the linear regression model

Abstract

This article introduces some Liu parameters in the linear regression model based on the work of Shukur, Månsson, and Sjölander. These methods of estimating the Liu parameter d increase the efficiency of Liu estimator. The comparison of proposed Liu parameters and available methods has done using Monte Carlo simulation and a real data set where the mean squared error, mean absolute error and interval estimation are considered as performance criterions. The simulation study shows that under certain conditions the proposed Liu parameters perform quite well as compared to the ordinary least squares estimator and other existing Liu parameters.     

On group divisible response surface (GDRS) designs

In this paper some experimental situations are identified corresponding to which suitable response surface designs do not exist. A class of response surface designs is introduced to cope with these situations. Their analysis with and without blocking and methods of construction is discussed.