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.     

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.     

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling(RSS) called moving extremes RSS(MERSS) is considered for the estimation of the scale and shape parameters for the log-logistic distribution. Several traditional estimators and ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared to the corresponding ones under SRS. The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.     

Tests of perfect judgment ranking using pseudo-samples

Ranked set sampling (RSS) is a sampling approach that can produce improved statistical inference when the ranking process is perfect. While some inferential RSS methods are robust to imperfect rankings, other methods may fail entirely or provide less efficiency. We develop a nonparametric procedure to assess whether the rankings of a given RSS are perfect. We generate pseudo-samples with a known ranking and use them to compare with the ranking of the given RSS sample. This is a general approach that can accommodate any type of raking, including perfect ranking. To generate pseudo-samples, we consider the given sample as the population and generate a perfect RSS. The test statistics can easily be implemented for balanced and unbalanced RSS. The proposed tests are compared using Monte Carlo simulation under different distributions and applied to a real data set.     

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.     

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.     

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.     

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.     

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 .     

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.     

至多一个分布变点的非参数统计推断

本文研究了连续分布函数变点的非参数统计推断问题.利用秩统计量和次序统计量,获得了变点的一种估计,不仅论证了点估计的强相合性,而且讨论了假设检验和区间估计.     

关于两总体均值差的一种半参数假设检验方法

近年来, 已有一些在半参数密度函数比模型下建立半参数统计分析方法的报道, 这些方法往往比参数方法稳健, 比非参数方法有效. 在本文里, 我们提出一种半参数的假设检验方法用于对两总体均值差进行假设检验. 该方法主要建立在对两总体均值差进行半参数估计的基础上. 我们报告了一些理论和统计模拟的结果, 得出该方法在数据符合正态性假设时, 比常用的参数和非参数方法略好; 而在数据不符合正态性假设时, 它的优势就非常明显. 我们还将提出的方法用到了两组真实数据的分析上.     

Constrained nonparametric estimation of the mean and the CDF using ranked-set sampling with a covariate

Ranked-set sampling (RSS) and judgment post-stratification (JPS) are related schemes in which more efficient statistical inference is obtained by creating a stratification based on ranking information. The rankings may be completely subjective, or they may be based on values of a covariate. Recent work has shown that regardless of how the rankings are done, the in-stratum cumulative distribution functions (CDFs) must satisfy certain constraints, and we show here that if the rankings are done according to a covariate, then tighter constraints must hold. We also show that under a mild stochastic ordering assumption, still tighter constraints must hold. Taking advantage of these new constraints leads to improved small-sample estimates of the in-stratum CDFs in all RSS and JPS settings. For JPS, the new constraints also lead to improved estimates of the overall CDF and the population mean.     

Wavelet-Based Estimation for Univariate Stable Laws

Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement. This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution. Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using simulated data, and an application to a real data example is explored. One novel aspect of this work is that here wavelets are being used to solve a parametric problem, rather than a nonparametric one, which is the more typical context in wavelet applications.     

A Computational Approach for Full Nonparametric Bayesian Inference Under Dirichlet Process Mixture Models

Widely used parametric generalized linear models are, unfortunately, a somewhat limited class of specifications. Nonparametric aspects are often introduced to enrich this class, resulting in semiparametric models. Focusing on single or k-sample problems, many classical nonparametric approaches are limited to hypothesis testing. Those that allow estimation are limited to certain functionals of the underlying distributions. Moreover, the associated inference often relies upon asymptotics when nonparametric specifications are often most appealing for smaller sample sizes. Bayesian nonparametric approaches avoid asymptotics but have, to date, been limited in the range of inference. Working with Dirichlet process priors, we overcome the limitations of existing simulation-based model fitting approaches which yield inference that is confined to posterior moments of linear functionals of the population distribution. This article provides a computational approach to obtain the entire posterior distribution for more general functionals. We illustrate with three applications: investigation of extreme value distributions associated with a single population, comparison of medians in a k-sample problem, and comparison of survival times from different populations under fairly heavy censoring.     

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.     

A Marginal Sampler for σ-Stable Poisson–Kingman Mixture Models

We investigate the class of σ-stable Poisson–Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs, which encompasses most of the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman–Yor process, the normalized inverse Gaussian process, and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterizations of σ-stable Poisson–Kingman RPMs can be usefully exploited for devising a Markov chain Monte Carlo (MCMC) algorithm for performing posterior inference with a Bayesian nonparametric mixture model. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a small number of auxiliary variables per iteration. We apply our sampling scheme to a density estimation and clustering tasks with unidimensional and multidimensional datasets, and compare it against competing MCMC sampling schemes. Supplementary materials for this article are available online.     

Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

We consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated.     

The super-efficiency procedure for outlier identification,not for ranking efficient units

In this paper, we conduct simulation experiments to evaluate the performance of two alternative uses of the super-efficiency procedure in Data Envelopment Analysis (DEA). The first is for outlier identification and the second is for ranking efficient units. We find that the ranking procedure does not perform satisfactorily. In fact, the correlations between the true efficiency and the estimated super-efficiency are negative for the subset of efficient observations, and the conventional DEA model performs as well as the super-efficiency DEA model when all observations are considered. However, when data are contaminated with outliers, the use of the super-efficiency model to identify and remove outliers results in more accurate efficiency estimates than those obtained from the conventional DEA estimation model.     

产品可靠寿命的最优排序集挑选设计

针对产品可靠寿命的估计问题,构造了基于排序集挑选样本的非参数估计量,证明了该估计量具有强相合性和渐近正态性。针对不同的可靠寿命,具体给出了使得估计效率达到最大的最优挑选抽样设计。最后,渐近相对效率和实际应用的研究结果表明:最优挑选设计的抽样效率高于简单随机抽样。