Non Asymptotic Minimax Estimation of Functionals with Noisy Observations

The minimax estimation of functionals by a finite number of noisy observations is considered. A new way to formalize the problem that enables one to calculate non asymptotic optimal estimates is proposed. The calculations can be turned into and executed as a computer algorithm or carried out analytically under week assumptions on random variables. Some examples are considered.     

Recent Data on the Number of Adoptions of Foster Children

ABSTRACT

Public agency adoption programs require accurate and current data to identify trends, project caseloads and costs, revise practice and develop financial incentive systems. The federal government and advocacy groups also need accurate and current statistics on adoption to formulate and implement major policy initiatives. Collection of data to establish baselines for the federal Adoption Incentive Program resulted in a re-examination of recent underestimates of the number of adoptions. The underestimates were produced by a convergence of factors including under-reporting by states, use of inappropriate data as the basis for the estimates, and real increases in the number of adoptions.     

On improvement in estimating the population mean in simple random sampling

Kadilar and Cingi [Ratio estimators in simple random sampling, Appl. Math. Comput. 151 (3) (2004), pp. 893–902] introduced some ratio-type estimators of finite population mean under simple random sampling. Recently, Kadilar and Cingi [New ratio estimators using correlation coefficient, Interstat 4 (2006), pp. 1–11] have suggested another form of ratio-type estimators by modifying the estimator developed by Singh and Tailor [Use of known correlation coefficient in estimating the finite population mean, Stat. Transit. 6 (2003), pp. 655–560]. Kadilar and Cingi [Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett. 19 (1) (2006), pp. 75–79] have suggested yet another class of ratio-type estimators by taking a weighted average of the two known classes of estimators referenced above. In this article, we propose an alternative form of ratio-type estimators which are better than the competing ratio, regression, and other ratio-type estimators considered here. The results are also supported by the analysis of three real data sets that were considered by Kadilar and Cingi.     

我国农业现代化发展水平评测研究综述

应用阅读法、评述法和归纳法对国内外20世纪90年代以来,尤其是近10年来定量研究农业现代化发展水平的成果进行梳理,从主要评价方法、指标系统的构建、指标权重的确定和目标值的确定4个维度对其进行归纳总结,探求农业现代化定量研究的规律。结果表明：目前国内农业现代化水平的定量研究应用最为广泛的方法是综合指标法;农业现代化评价有5个基本步骤;农业现代化评价指标体系一般包括农业生产条件等版块;评价指标标准值确定要动态化、紧密结合当地实际且要反映变化趋势。农业现代化定量研究中尚存在的问题是数据搜集和整理困难、对国外相关资料缺乏挖掘以及新的评价方法和工具亟待引入。     

论中小企业的国际化经营道路

为了寻求经营机会、保护和扩大原有市场、克服贸易壁垒、追求优惠政策和获取技术 ,走国际化经营之路已成为中小企业的战略选择。目前中小企业已成为我国企业国际化经营的一个重要组成部分 ,直接影响到我国开放型经济战略的实现。文章阐述了中小企业国际化经营的客观必然性 ,并分析了其经营策略和道路     

线性抛物型方程的窄四边形元逼近方法

讨论了一类发展方程——线性抛物型方程的窄四边形元逼近方法,导出了相应的半离散格式和全离散格式,并通过一些新的技巧,得到了相应的误差估计.     

Asymptotically optimal shrinkage estimates for non-normal data

Motivated by several practical issues, we consider the problem of estimating the mean of a p-variate population (not necessarily normal) with unknown finite covariance. A quadratic loss function is used. We give a number of estimators (for the mean) with their loss functions admitting expansions to the order of p ^?1/2 as p→∞. These estimators contain Stein's [Inadmissibility of the usual estimator for the mean of a multivariate normal population, in Proceedings of the Third Berkeley Symposium in Mathematical Statistics and Probability, Vol. 1, J. Neyman, ed., University of California Press, Berkeley, 1956, pp. 197–206] estimate as a particular case and also contain ‘multiple shrinkage’ estimates improving on Stein's estimate. Finally, we perform a simulation study to compare the different estimates.     

Likelihood estimation for a general class of inverse exponentiated distributions based on complete and progressively censored data

In this paper, we establish the existence and uniqueness of the maximum-likelihood estimates of the parameters of a general class of inverse exponentiated distributions based on complete as well as progressively Type-I and Type-II censored data.     

Bayesian inference for the randomly censored Weibull distribution

In this paper, we consider the Bayesian inference of the unknown parameters of the randomly censored Weibull distribution. A joint conjugate prior on the model parameters does not exist; we assume that the parameters have independent gamma priors. Since closed-form expressions for the Bayes estimators cannot be obtained, we use Lindley's approximation, importance sampling and Gibbs sampling techniques to obtain the approximate Bayes estimates and the corresponding credible intervals. A simulation study is performed to observe the behaviour of the proposed estimators. A real data analysis is presented for illustrative purposes.     

A pool-adjacent-violators-algorithm approach to detect infinite parameter estimates in one-regressor dose–response models with asymptotes

Binary response models are often applied in dose–response settings where the number of dose levels is limited. Commonly, one can find cases where the maximum likelihood estimation process for these models produces infinite values for at least one of the parameters, often corresponding to the ‘separated data’ issue. Algorithms for detecting such data have been proposed, but are usually incorporated directly into in the parameter estimation. Additionally, they do not consider the use of asymptotes in the model formulation. In order to study this phenomenon in greater detail, we define the class of specifiably degenerate functions where this can occur (including the popular logistic and Weibull models) that allows for asymptotes in the dose–response specification. We demonstrate for this class that the well-known pool-adjacent-violators algorithm can efficiently pre-screen for non-estimable data. A simulation study demonstrates the frequency with which this problem can occur for various response models and conditions.