优良抽样设计下Logistic分布中参数的极大似然估计

当研究目标的实际测量具有不可修复的破坏性或耗资巨大时,有效的抽样设计将是一项重要的研究课题.在统计推断方面,排序集抽样(RSS)被视为一种比简单随机抽样(SRS)更为有效的收集数据的方式.动态极值RSS (MERSS)是一种修正的RSS.文章在SRS和MERSS下研究了Logistic分布中参数的极大似然估计(MLEs).在这两种抽样下证明了该分布中位置参数和刻度参数的MLEs的存在性和唯一性,并计算了所含参数的Fisher信息量和Fisher信息矩阵.比较了这两种抽样下对应估计的渐近效率.数值结果表明MERSS下的MLEs一致优于SRS下的MLEs.     

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research 3, 385-390]as an effective way to estimate the pasture mean. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling(MERSS) is considered for the best linear unbiased estimators(BLUEs) for the simple linear regression model. The BLUEs for this model under MERSS are derived. The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.     

Estimation of the Common Mean of a Bivariate Normal Population

In this paper we discuss the problem of estimating the common mean of a bivariate normal population based on paired data as well as data on one of the marginals. Two double sampling schemes with the second stage sampling being either a simple random sampling (SRS) or a ranked set sampling (RSS) are considered. Two common mean estimators are proposed. It is found that under normality, the proposed RSS common mean estimator is always superior to the proposed SRS common mean estimator and other existing estimators such as the RSS regression estimator proposed by Yu and Lam (1997, Biometrics, 53, 1070–1080). The problem of estimating the mean Reid Vapor Pressure (RVP) of regular gasoline based on field and laboratory data is considered.     

Empirical likelihood for balanced ranked-set sampled data

Ranked-set sampling (RSS) often provides more efficient inference than simple random sampling (SRS). In this article, we propose a systematic nonparametric technique, RSS-EL, for hypothesis testing and interval estimation with balanced RSS data using empirical likelihood (EL). We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations. In all three cases, RSS is shown to provide more efficient inference than SRS of the same size. Moreover, the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data, such as perfect ranking, identical ranking scheme in two groups, and location shift between two population distributions. The merit of the RSS-EL method is also demonstrated through simulation studies. This work was supported by National Natural Science Foundation of China (Grant No. 10871037)     

Proportion estimation in ranked set sampling in the presence of tie information

Ranked set sampling (RSS) is a statistical technique that uses auxiliary ranking information of unmeasured sample units in an attempt to select a more representative sample that provides better estimation of population parameters than simple random sampling. However, the use of RSS can be hampered by the fact that a complete ranking of units in each set must be specified when implementing RSS. Recently, to allow ties declared as needed, Frey (Environ Ecol Stat 19(3):309–326, 2012) proposed a modification of RSS, which is to simply break ties at random so that a standard ranked set sample is obtained, and meanwhile record the tie structure for use in estimation. Under this RSS variation, several mean estimators were developed and their performance was compared via simulation, with focus on continuous outcome variables. We extend the work of Frey (2012) to binary outcomes and investigate three nonparametric and three likelihood-based proportion estimators (with/without utilizing tie information), among which four are directly extended from existing estimators and the other two are novel. Under different tie-generating mechanisms, we compare the performance of these estimators and draw conclusions based on both simulation and a data example about breast cancer prevalence. Suggestions are made about the choice of the proportion estimator in general.     

基于有序抽样样本的参数的极大似然估计的性质

有序抽样是一种新的抽样方法 ,与简单随机抽样方法相比它具有很多很好的性质 .本文讨论了在有序抽样样本下的参数的极大似然估计的性质 .     

Modified Maximum Likelihood Estimators Based on Ranked Set Samples

The maximum livelihood estimator (MLE) using a ranked set sample (RSS) usually has no closed expression because the maximum likelihood equation involves both hazard and inverse hazard functions, and may no longer be efficient when the judgment ranking is imperfect. In this paper, we consider a modified MLE (MMLE) using RSS for general parameters, which has the same expression as the MLE using a simple random sample (SRS), except that the SRS in the MLE is replaced by the RSS. The results show that, for the location parameter, the MMLE is always more efficient than the MLE using SRS, and for the scale parameter, the MMLE is at least as efficient as the MLE using SRS, when the same sample size is used. Under the perfect judgment ranking, numerical examples also show that the MMLE has good efficiency relative to the MLE based on RSS. When the judgment error is present, we conduct simulations to show that the MMLE is more robust than the MLE using RSS.     

Wilcoxon signed rank test using ranked-set sample

Ranked-set sampling is useful when measurements are destructive or costly to obtain but ranking of the observations is relatively easy. The Wilcoxon signed rank test statistic based on the ranked-set sample is considered. We compared the asymptotic relative efficiencies of the RSS Wilcoxon signed rank test statistic with respect to the SRS Wilcoxon signed rank test statistic and the RSS sign test statistic. Throughout the ARE’s, the proposed test statistic is superior to the SRS Wilcoxon signed rank test statistic and the RSS sign test statistic.     

Group sequential comparison of two binomial proportions under ranked set sampling design

Ranked set sampling (RSS) is a technique for incorporating auxiliary (concomitant) information into estimation and testing procedures right at the design stage. In this paper, we propose group sequential testing procedures for comparing two treatments with binary outcomes under an RSS scheme with perfect ranking. We compare the power, the average sample sizes and type I errors of the proposed tests to those of the group sequential tests based on simple random sampling schemes. We illustrate the usefulness of the methodology by using data from a clinical trial on leukemia.     

Constrained estimation using judgment post-stratification

In ranked-set sampling (RSS) and judgment post-stratification (JPS), more efficient inference is obtained by creating a stratification based on ranking information. Using this stratification exactly as is done in stratified sampling or standard post-stratification leads to the standard nonparametric estimators for RSS and JPS. However, we show that strata obtained from ranking information satisfy additional constraints that need not be met by ordinary strata. Specifically, the in-stratum cumulative distribution functions (CDFs) can be no more extreme, in a certain sense, than the CDFs for order statistics from the overall distribution. The additional constraints can be used to obtain better small-sample estimates of the in-stratum CDFs using either RSS or JPS. In the JPS case, the constraints also lead to better small-sample estimates of the overall CDF and the population mean.     

Quantile estimation under successive sampling

This paper deals with the estimation, under sampling in two successive occasions, of a finite population quantile. For this sampling design a class of estimators is proposed whose the ratio and difference estimators are particular cases. Asymptotic variance formulae are derived for the proposed estimators, and the optimal matching fraction is discussed. Comparisons are made with existing estimators in a simulation study using a natural population.     

Bayes minimax estimators of the mean of a scale mixture of multivariate normal distributions

Bayes estimation of the mean of a variance mixture of multivariate normal distributions is considered under sum of squared errors loss. We find broad class of priors (also in the variance mixture of normal class) which result in proper and generalized Bayes minimax estimators. This paper extends the results of Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264] in a manner similar to that of Maruyama [Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distribution, J. Multivariate Anal. 21 (2003) 69-78] but somewhat more in the spirit of Fourdrinier et al. [On the construction of bayes minimax estimators, Ann. Statist. 26 (1998) 660-671] for the normal case, in the sense that we construct classes of priors giving rise to minimaxity. A feature of this paper is that in certain cases we are able to construct proper Bayes minimax estimators satisfying the properties and bounds in Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264]. We also give some insight into why Strawderman's results do or do not seem to apply in certain cases. In cases where it does not apply, we give minimax estimators based on Berger's [Minimax estimation of location vectors for a wide class of densities, Ann. Statist. 3 (1975) 1318-1328] results. A main condition for minimaxity is that the mixing distributions of the sampling distribution and the prior distribution satisfy a monotone likelihood ratio property with respect to a scale parameter.     

利用分层抽样数据中完全辅助信息的模型校正方法

In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG).     

优良抽样设计下总体均值的比率估计

当研究目标的实际测量具有不可修复的破坏性或耗资巨大时,有效的抽样设计将是一项重要的研究课题.在统计推断方面,排序集抽样被视为一种更为有效的收集数据的方式.极值排序集抽样(ERSS)是一种改进的排序集抽样.文章在ERSS下研究了总体均值的比率估计.以正态分布为例,比较了简单随机抽样和ERSS下比率估计的相对效率.数值结果表明ERSS下的比率估计优于简单随机抽样下的比率估计.     

Construction of improved estimators in multiparameter estimation for continuous exponential families

A unified theory of simultaneous estimation of parameters for the continuous exponential family is presented. Estimators are constructed that improve on the standard ones (the maximum likelihood, UMVUE or best invariant estimator). These improved estimators shift the standard ones towards possibly non-zero points or data based points.     

Inference for a simple step-stress model based on ordered ranked set sampling

In this paper, we considered the inference problem on simple step-stress accelerated life test data from one-parameter exponential distribution under type-I censored ordered ranked set sample with cumulative exposure model. The Bayesian estimators and credible intervals for the model parameters are developed and compared with the corresponding estimators based on simple random sampling. Two real data sets and numerical simulation evaluations are presented to illustrate all the results developed here. The simulation study indicated that the proposed Bayes estimators and credible intervals based on ordered ranked set sampling performed better than their counterparts using simple random sampling.     

辅助信息下的逆抽样设计算法

通过将逆抽样设计视为一种特殊的二重抽样,建立了二重抽样和为回归估计的二重抽样的一般形式,得到了逆抽样设计算法下的回归估计.模拟分析的结果表明,以回归估计的形式引入较为合适的辅助信息,能够在估计精度上对逆抽样设计算法做出改进.     

正态-逆Wishart先验下多元线性模型中经验Bayes估计的优良性

在正态-逆Wishart先验下研究了多元线性模型中参数的经验Bayes估计及其优良性问题.当先验分布中含有未知参数时,构造了回归系数矩阵和误差方差矩阵的经验Bayes估计,并在Bayes均方误差(简称BMSE)准则和Bayes均方误差阵(简称BMSEM)准则下,证明了经验Bayes估计优于最小二乘估计.最后,进行了Monte Carlo模拟研究,进一步验证了理论结果.     

基于轮换样本连续性调查的校准组合估计方法研究

校准估计是抽样调查中比较常用的一种利用辅助信息提高估计量精度的方法。回归组合估计量作为轮换样本连续性调查中使用的一种有效的估计量,是可以通过校准程序得到的。基于回归组合估计量和校准程序之间的关系,本文提出了轮换样本连续性抽样调查条件下的不同校准组合估计量及其方差估计。校准组合估计量的主要思想是在校准估计程序中将拼配样本和非拼配样本的辅助信息进行不同的组合利用。本文利用美国现时人口调查的微观数据进行数值模拟,来比较不同校准组合估计量的估计效率,模拟结果表明两步校准组合估计量和两步校准双组合估计量的表现相似,且估计精度都高于H-T估计量及回归组合估计量;而两步校准组合估计量由于其简便性更适合应用于实践中。最后以我国农村住户连续性抽样调查为例,设计一套符合我国实际的轮换样本连续性调查方案,并将提出的校准组合估计量运用于估计阶段,为中国政府统计调查提供一定的借鉴和参考.     

A Class of Linear Biased Estimators of Regression ParameterMatrix in the Growth Curve Model

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