Ordered Random Fractions For Chronological Sampling

The method was devised for use in reference testing under the Average Quantity System, but appears to be of more general interest. It is useful where a chronological list of sampling points is required, as in sampling over time or from items in a line.     

Two-Stage Cluster Sampling with Ranked Set Sampling in the Secondary Sampling Frame

Motivated by a real-life problem, we develop a Two-Stage Cluster Sampling with Ranked Set Sampling (TSCRSS) design in the second stage for which we derive an unbiased estimator of population mean and its variance. An unbiased estimator of the variance of mean estimator is also derived. It is proved that the TSCRSS is more efficient—in the sense of having smaller variance—than the conventional two-stage cluster simple random sampling in which the second-stage sampling is with replacement. Using a simulation study on a real-life population, we show that the TSCRSS is more efficient than the conventional two-stage cluster sampling when simple random sampling without replacement is used in both stages.     

使用普查数据模拟MPPS抽样方法的研究

MPPS抽样即多变量与规模成比例的概率抽样,是20世纪90年代才提出来的一种抽样设计。近年来,中国有关部门与美国农业部国家农业署合作,进行了MPPS抽样设计的试点,来解决多目标调查问题。但是MPPS抽样在中国的应用非常有限。对MPPS抽样进行简单的回顾,介绍了它的基本估计,并对其应用进行了数据模拟研究。模拟中采用了系统抽样和泊松抽样的方法,根据实际调查数据得到了明确的结果。还对泊松抽样的一种变形永久随机数抽样的方法进行了模拟研究,并对它的一种误用情况进行了模拟比较,得到了具有说服力的结果。     

A Class of Normalized Random Measures with an Exact Predictive Sampling Scheme

Abstract. In this article, we define and investigate a novel class of non‐parametric prior distributions, termed the class . Such class of priors is dense with respect to the homogeneous normalized random measures with independent increments and it is characterized by a richer predictive structure than those arising from other widely used priors. Our interest in the class is mainly motivated by Bayesian non‐parametric analysis of some species sampling problems concerning the evaluation of the species relative abundances in a population. We study both the probability distribution of the number of species present in a sample and the probability of discovering a new species conditionally on an observed sample. Finally, by using the coupling from the past method, we provide an exact sampling scheme for the system of predictive distributions characterizing the class .     

Calibration Weighting in Stratified Random Sampling

A new calibration estimator is proposed to estimate the population mean in the stratified random sampling. The corrected expression of Tracy et al. (2003) calibrated weights are presented and new improved calibration weights are introduced. Theoretical variance of the suggested estimator is discussed. Also a simulation study is carried out to show the properties of the proposed estimator.     

Sampling from spatial databases

This paper deals with techniques for obtaining random point samples from spatial databases. We seek random points from a continuous domain (usually ²) which satisfy a spatial predicate that is represented in the database as a collection of polygons. Several applications of spatial sampling (e.g. environmental monitoring, agronomy, forestry, etc) are described. Sampling problems are characterized in terms of two key parameters: coverage (selectivity), and expected stabbing number (overlap). We discuss two fundamental approaches to sampling with spatial predicates, depending on whether we sample first or evaluate the predicate first. The approaches are described in the context of both quadtrees and R-trees, detailing the sample first, acceptance/rejection tree, and partial area tree algorithms. A sequential algorithm, the one-pass spatial reservoir algorithm is also described. The relative performance of the various sampling algorithms is compared and choice of preferred algorithms is suggested. We conclude with a short discussion of possible extensions.     

Improvement in Estimating the Population Median in Simple Random Sampling and Stratified Random Sampling Using Auxiliary Information

This paper deals with estimation of population median in simple and stratified random samplings by using auxiliary information. Auxiliary information is rarely used in estimating population median, although there have been many studies to estimate population mean using auxiliary information. In this study, we suggest some estimators using auxiliary information such as mode and range of an auxiliary variable and correlation coefficient. We also expand these estimators to stratified random sampling for combined and separate estimators. We obtain mean square error equations for all proposed estimators and find theoretical conditions. These conditions are also supported by using numerical examples.     

Conditional and Restricted Pareto Sampling: Two New Methods for Unequal Probability Sampling

Abstract. Two new unequal probability sampling methods are introduced: conditional and restricted Pareto sampling. The advantage of conditional Pareto sampling compared with standard Pareto sampling, introduced by Rosén (J. Statist. Plann. Inference, 62, 1997, 135, 159), is that the factual inclusion probabilities better agree with the desired ones. Restricted Pareto sampling, preferably conditioned or adjusted, is able to handle cases where there are several restrictions on the sample and is an alternative to the recent cube method for balanced sampling introduced by Deville and Tillé (Biometrika, 91, 2004, 893). The new sampling designs have high entropy and the involved random numbers can be seen as permanent random numbers.     

Selected Ranked Set Sampling

This paper proposes a sampling procedure called selected ranked set sampling (SRSS), in which only selected observations from a ranked set sample (RSS) are measured. This paper describes the optimal linear estimation of location and scale parameters based on SRSS, and for some distributions it presents the required tables for optimal selections. For these distributions, the optimal SRSS estimators are compared with the other popular simple random sample (SRS) and RSS estimators. In every situation the estimators based on SRSS are found advantageous at least in some respect, compared to those obtained from SRS or RSS. The SRSS method with errors in ranking is also described. The relative precision of the estimator of the population mean is investigated for different degrees of correlations between the actual and erroneous ranking. The paper reports the minimum value of the correlation coefficient between the actual and the erroneous ranking required for achieving better precision with respect to the usual SRS estimator and with respect to the RSS estimator.     

Length-Biassed Sampling from a Finite Population

Expressions are derived for the interval moments of a length-biassed sample from a renewal process of finite length.     

Estimation of Finite Population Mean in Stratified Random Sampling with Two Auxiliary Variables under Double Sampling Design

In this article, a chain ratio-product type exponential estimator is proposed for estimating finite population mean in stratified random sampling with two auxiliary variables under double sampling design. Theoretical and empirical results show that the proposed estimator is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Chand (1975) chain ratio estimator, Choudhary and Singh (2012) estimator, chain ratio-product-type estimator, Sahoo et al. (1993) difference type estimator, and Kiregyera (1984) regression-type estimator. Two data sets are used to illustrate the performances of different estimators.     

A New Formula for Inclusion Probabilities in Median-Ranked Set Sampling

This article develops a new generalized formula to compute the inclusion probabilities of a median-ranked set sample in a finite population setting. The use of this formula is illustrated in a numerical example. Furthermore, the inclusion probabilities of a median-ranked set sample is compared with the inclusion probabilities of ranked set and simple random samples.     

Multivariate Poisson hidden Markov models with a case study of modelling seismicity

While the literature on multivariate models for continuous data flourishes, there is a lack of models for multivariate counts. We aim to contribute to this framework by extending the well known class of univariate hidden Markov models to the multidimensional case, by introducing multivariate Poisson hidden Markov models. Each state of the extended model is associated with a different multivariate discrete distribution. We consider different distributions with Poisson marginals, starting from the multivariate Poisson distribution and then extending to copula based distributions to allow flexible dependence structures. An EM type algorithm is developed for maximum likelihood estimation. A real data application is presented to illustrate the usefulness of the proposed models. In particular, we apply the models to the occurrence of strong earthquakes (surface wave magnitude ≥5), in three seismogenic subregions in the broad region of the North Aegean Sea for the time period from 1 January 1981 to 31 December 2008. Earthquakes occurring in one subregion may trigger events in adjacent ones and hence the observed time series of events are cross‐correlated. It is evident from the results that the three subregions interact with each other at times differing by up to a few months. This migration of seismic activity is captured by the model as a transition to a state of higher seismicity.     

A class of maximum-entropy multivariate distributions

This paper characterizes a class of multivariate distributions that includes the multinormal and is contained in the exponential family. The wide range of possible applications of these distributions is suggested by some of hte characteristics germane to them: First, they maximize Shannon's entropy among all distributions that have finite moments of given orders. As such, they constitute a class of distributions that includes the multinormal and some likely alternatives. Second, they can exhibit several modes, and, further-more, they do so with a relatively small number of parameters (compared to mixtures of multinormals). Third, they are the stationary distributions of certain diffusion processes. Fourth, they approximate, near the multinormal, the multivariate Pearson family. And fifth, the maximum likelihood estimators of their population moments are the sample moments. Two possible methods of estimating the distributions are studied in this paper: maximum likelihood estimation, and a fast procedure that can be used to find consistent estimators of the parameters via sample moments. A FORTTAN subroutine that implements the latter method is also provided.     

辅以排序集样本的分层抽样方法研究

分层抽样中,样本在各层中的不同获取方式会对估计量的精度和试验费用产生一定的影响,而已有的理论方法大多不能在提高精度的同时降低调查费用。为此,将排序抽样与分层抽样方法相结合,提出了辅以排序集样本的分层抽样方案,并得到了总体均值的估计量以及这一估计量的良好性质。这些结果表明,与单一的分层随机抽样相比,这种抽样设计的估计量具有更高的精度,同时也节约了各层抽样调查的费用。     

A List Sequential Sampling Method Suitable for Real-Time Sampling

Abstract.  A flexible list sequential π ps sampling method is introduced and studied. It can reproduce any given sampling design without replacement, of fixed or random sample size. The method is a splitting method and uses successive updating of inclusion probabilities. The main advantage of the method is in real-time sampling situations where it can be used as a powerful alternative to Bernoulli and Poisson sampling and can give any desired second-order inclusion probabilities and thus considerably reduce the variability of the sample size.     

Markov Chain Monte Carlo in small worlds

As the number of applications for Markov Chain Monte Carlo (MCMC) grows, the power of these methods as well as their shortcomings become more apparent. While MCMC yields an almost automatic way to sample a space according to some distribution, its implementations often fall short of this task as they may lead to chains which converge too slowly or get trapped within one mode of a multi-modal space. Moreover, it may be difficult to determine if a chain is only sampling a certain area of the space or if it has indeed reached stationarity. In this paper, we show how a simple modification of the proposal mechanism results in faster convergence of the chain and helps to circumvent the problems described above. This mechanism, which is based on an idea from the field of “small-world” networks, amounts to adding occasional “wild” proposals to any local proposal scheme. We demonstrate through both theory and extensive simulations, that these new proposal distributions can greatly outperform the traditional local proposals when it comes to exploring complex heterogenous spaces and multi-modal distributions. Our method can easily be applied to most, if not all, problems involving MCMC and unlike many other remedies which improve the performance of MCMC it preserves the simplicity of the underlying algorithm.     

Star-Type Systematic Sampling Schemes for Finite Populations

Two new sampling schemes namely, Star-Type Systematic (STS) sampling without replacement and Modified Star-Type Systematic (MSTS) sampling without replacement for estimation of finite population means are introduced. The relative performances of the proposed star-type systematic sample means along with those of the simple random and systematic sample means are assessed for a hypothetical population with a linear trend and also for certain natural populations. Furthermore, the usefulness of the proposed sampling schemes in quality control and for constructing partial diallel crosses in mating designs are briefly break discussed.     

Markov Chains and De-initializing Processes

We define a notion of de-initializing Markov chains. We prove that to analyse convergence of Markov chains to stationarity, it suffices to analyse convergence of a de-initializing chain. Applications are given to Markov chain Monte Carlo algorithms and to convergence diagnostics.     

Importance Sampling for Sums of Lognormal Distributions with Applications to Operational Risk

In this paper we use Importance Sampling to estimate tail probabilities for a finite sum of lognormal distributions. We use a defensive mixture, and develop a method of choosing the parameters via the EM algorithm; we also consider the technique which assumes the importance sampling density to belong to the same parametric family of the random variables to be summed. In both cases, the instrumental density is found by minimizing Cross-Entropy. A comparison based on several simulation experiments shows that the defensive mixture has the best performance. Finally, we study the Poisson-lognormal compound distribution framework and present a real-data application.