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.     

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.     

Markov Chain Sampling Methods for Dirichlet Process Mixture Models

Abstract

This article reviews Markov chain methods for sampling from the posterior distribution of a Dirichlet process mixture model and presents two new classes of methods. One new approach is to make Metropolis—Hastings updates of the indicators specifying which mixture component is associated with each observation, perhaps supplemented with a partial form of Gibbs sampling. The other new approach extends Gibbs sampling for these indicators by using a set of auxiliary parameters. These methods are simple to implement and are more efficient than previous ways of handling general Dirichlet process mixture models with non-conjugate priors.     

Conditional Inference on Tables With Structural Zeros

We develop a set of sequential importance sampling (SIS) strategies for sampling nearly uniformly from two-way zero-one or contingency tables with fixed marginal sums and a given set of structural zeros. The SIS procedure samples tables column by column or cell by cell by using appropriate proposal distributions, and enables us to approximate closely the null distributions of a number of test statistics involved in such tables. When structural zeros are on the diagonal or follow certain patterns, more efficient SIS algorithms are developed which guarantee that every generated table is valid. Examples show that our methods can be applied to make conditional inference on zero-one and contingency tables, and are more efficient than other existing Monte Carlo algorithms.     

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.     

A new resampling method for sampling designs without replacement: the doubled half bootstrap

A new and very fast method of bootstrap for sampling without replacement from a finite population is proposed. This method can be used to estimate the variance in sampling with unequal inclusion probabilities and does not require artificial populations or utilization of bootstrap weights. The bootstrap samples are directly selected from the original sample. The bootstrap procedure contains two steps: in the first step, units are selected once with Poisson sampling using the same inclusion probabilities as the original design. In the second step, amongst the non-selected units, half of the units are randomly selected twice. This procedure enables us to efficiently estimate the variance. A set of simulations show the advantages of this new resampling method.     

Sampling Expansions and Interpolation in Unitarily Translation Invariant Reproducing Kernel Hilbert Spaces

Sufficient conditions are established in order that, for a fixed infinite set of sampling points on the full line, a function satisfies a sampling theorem on a suitable closed subspace of a unitarily translation invariant reproducing kernel Hilbert space. A number of examples of such reproducing kernel Hilbert spaces and the corresponding sampling expansions are given. Sampling theorems for functions on the half-line are also established in RKHS using Riesz bases in subspaces of L ²(R ⁺).     

On progressively first failure censored Lindley distribution

This article deals with the progressively first failure censored Lindley distribution. Maximum likelihood and Bayes estimators of the parameter and reliability characteristics of Lindley distribution based on progressively first failure censored samples are derived. Asymptotic confidence intervals based on observed Fisher information and bootstrap confidence intervals of the parameter are constructed. Bayes estimators using non-informative and gamma informative priors are derived using importance sampling procedure and Metropolis–Hastings (MH) algorithm under squared error loss function. Also, HPD credible intervals based on importance sampling procedure and MH algorithm for the parameter are constructed. To study the performance of various estimators discussed in this article, a Monte Carlo simulation study is conducted. Finally, a real data set is studied for illustration purposes.     

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.     

基于中位数排序集抽样的非参数估计

本文提出中位数排序集抽样下总体中位数的非参数估计,证明了这种估计具有强相合性和渐近正态性,并系统验证了新估计量的功效一致优于排序集抽样下和简单随机抽样下总体中位数的估计量。最后,我们对针叶树的一组真实数据进行了实际应用。     

Rounded data analysis based on multi-layer ranked set sampling

Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It shows that the rounding errors seriously distort the behavior of covariance matrix estimate, and lead to inconsistent estimation. Taking this into account, we present a new approach to implement the estimation for this model, and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that our estimates based on rounded multi-layer ranked set sampling are always more efficient than those based on rounded simple random sampling.     

On the Ranked-Set Sampling M-Estimates for Symmetric Location Families

The ranked-set sampling (RSS) is applicable in practical problems where the variable of interest for an observed item is costly or time-consuming but the ranking of a set of items according to the variable can be easily done without actual measurement. In this article, the M-estimates of location parameters using RSS data are studied. We deal mainly with symmetric location families. The asymptotic properties of M-estimates based on ranked-set samples are established. The properties of unbalanced ranked-set sample M-estimates are employed to develop the methodology for determining optimal ranked-set sampling schemes. The asymptotic relative efficiencies of ranked-set sample M-estimates are investigated. Some simulation studies are reported.     

Limit-periodic Verblunsky coefficients for orthogonal polynomials on the unit circle

Avila recently introduced a new method for the study of the discrete Schrödinger operator with limit-periodic potential. I adapt this method to the context of orthogonal polynomials in the unit circle with limit-periodic Verblunsky coefficients. Specifically, I represent these two-sided Verblunsky coefficients as a continuous sampling of the orbits of a Cantor group by a minimal translation. I then investigate the measures that arise on the unit circle as I vary the sampling function. I show that generically the spectrum is a Cantor set and we have empty point spectrum. Furthermore, there exists a dense set of sampling functions for which the corresponding spectrum is a Cantor set of positive Lebesgue measure, and all corresponding spectral measures are purely absolutely continuous.     

Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling

Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we consider ranked set sampling, in which ranking of units are done based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We then estimate the mean of the study variate Y by the BLUE based on the measurements made on the units of the ranked set sampling regarding the study variable Y, when (X ,Y) follows a Morgenstern type bivariate exponential distribution. We then consider unbalanced multistage ranked set sampling and estimate the mean of the study variate Y by the BLUE based on the observations made on the units of multistage ranked set sample regarding the study variable Y. Efficiency comparison is also made on all estimators considered in this work.     

排序集抽样下指数分布的产品可靠度研究

为了提高指数分布产品可靠度的估计效率,研究了基于排序集抽样方法的极大似然估计量(Maximum likelihood estimator,MLE),证明了新MLE具有存在性、唯一性和渐近正态性,并通过排序集样本的Fisher信息得到MLE的渐近方差。针对似然方程没有显式解的问题,利用部分期望法对MLE进行修正,并给出其具体表达式。渐近相对效率和模拟相对效率的研究结果表明:排序集抽样下MLE和修正MLE的估计效率都一致高于简单随机抽样下MLE。最后,将推荐方法应用到转移性肾癌的临床研究中。     

Universal sampling,quasicrystals and bounded remainder sets

We examine the result due to Matei and Meyer that simple quasicrystals are universal sampling sets, in the critical case when the density of the sampling set is equal to the measure of the spectrum. We show that in this case, an arithmetical condition on the quasicrystal determines whether it is a universal set of “stable and non-redundant” sampling.     

Dynamic importance sampling in Bayesian networks based on probability trees

In this paper we introduce a new dynamic importance sampling propagation algorithm for Bayesian networks. Importance sampling is based on using an auxiliary sampling distribution from which a set of configurations of the variables in the network is drawn, and the performance of the algorithm depends on the variance of the weights associated with the simulated configurations. The basic idea of dynamic importance sampling is to use the simulation of a configuration to modify the sampling distribution in order to improve its quality and so reducing the variance of the future weights. The paper shows that this can be achieved with a low computational effort. The experiments carried out show that the final results can be very good even in the case that the initial sampling distribution is far away from the optimum.     

Approximating connected facility location with buy-at-bulk edge costs via random sampling

In the connected facility location problem with buy-at-bulk edge costs we are given a set of clients with positive demands and a set of potential facilities with opening costs in an undirected graph with edge lengths obeying the triangle inequality. Moreover, we are given a set of access cable types, each with a cost per unit length and a capacity such that the cost per capacity decreases from small to large cables, and a core cable type of infinite capacity. The task is to open some facilities and to connect them by a Steiner tree using core cables, and to build a forest network using access cables such that the edge capacities suffice to simultaneously route all client demands unsplit to the open facilities. The objective is to minimize the total cost of opening facilities, building the core Steiner tree, and installing the access cables. In this paper, we devise a constant-factor approximation algorithm for this problem based on a random sampling technique.     

不完美排序集抽样的符号检验

实际应用排序集抽样时,主观排序总是会出现误差。本文考虑了不完美排序对最优抽样下分位数符号检验的影响,并且给出不同分位数的误差函数图像,以便具体应用时参考。     

Oblique Projections and Sampling Problems

In this work, the consistent sampling requirement of signals is studied. We establish how this notion is related with certain set of projectors which are selfadjoint with respect to a semi-inner product. We extend previous results and present some new problems related with sampling theory.