A theoretical analysis of the power of biased coin designs

Outlining some recently obtained results of Hu and Rosenberger [2003. Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc. 98, 671–678] and Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835] on the relationship between sequential randomized designs and the power of the usual statistical procedures for testing the equivalence of two competing treatments, the aim of this paper is to provide theoretical proofs of the numerical results of Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835]. Furthermore, we prove that the Adjustable Biased Coin Design [Baldi Antognini A., Giovagnoli, A., 2004. A new “biased coin design” for the sequential allocation of two treatments. J. Roy. Statist. Soc. Ser. C 53, 651–664] is uniformly more powerful than the other “coin” designs proposed in the literature for any sample size.     

Multi-phase sampling under cost constraints

Multi-phase sampling (M-PhS) scheme is useful when the interest is in the estimation of the population mean of an expensive variable strictly connected with other cheaper (auxiliary) variables. The MSE is an accuracy measure of an estimator. Usually it decreases as the sample size increases. In practice the sample size cannot become arbitrarily large for possible cost constraints. From a practical point of view it would be useful to know the sample sizes which guarantee the best accuracy of the estimates for fixed costs. These “optimum” sample sizes can be, in some cases, computable but not admissible. In other cases, they can be neither admissible nor computable. The main goal of this paper is to propose a solution for both these situations. It will be clear that in both situations the solution is to consider a M-PhS scheme with one or more phases less.     

Theory & Methods: Incomplete detection in enumeration surveys: Whither distance sampling?

This paper considers the problem of undercount or incomplete detection in enumeration surveys that are intended to estimate population counts or population abundance. The problem is widespread in ecology but also occurs in other surveys: the census undercount is a well-known example of the problem. After framing the problem in a general context, the paper focuses on line transect sampling and the distance sampling method which has been widely applied in surveys of ecological populations. It describes distance sampling data and presents a graphical derivation of the distance sampling estimator. The graphical analysis leads to a new expression for the distance sampling estimator which gives useful insights into the nature of the estimator. The paper discusses the uniformity assumption on which distance sampling depends and describes the properties of the distance sampling estimator when uniformity does not hold. It then explores the relationship between this and other evaluations of distance sampling and mentions briefly some statistical ideas for treating the general incomplete detection problem. The paper concludes with some reflections on general insights arising from the research.     

永久随机数在多层次调查中的应用

采用永久随机数法抽样技术抽到的样本具有很好地样本兼容的性质。本文讨论了采用序贯srswor抽样技术和Poisson抽样技术这两种永久随机数法抽样技术时,多层次调查的实现问题,希望能为多层次调查的实现提供一点启示。     

Semiparametric Time-Varying Coefficients Regression Model for Longitudinal Data

Abstract.  In this paper, we consider a semiparametric time-varying coefficients regression model where the influences of some covariates vary non-parametrically with time while the effects of the remaining covariates follow certain parametric functions of time. The weighted least squares type estimators for the unknown parameters of the parametric coefficient functions as well as the estimators for the non-parametric coefficient functions are developed. We show that the kernel smoothing that avoids modelling of the sampling times is asymptotically more efficient than a single nearest neighbour smoothing that depends on the estimation of the sampling model. The asymptotic optimal bandwidth is also derived. A hypothesis testing procedure is proposed to test whether some covariate effects follow certain parametric forms. Simulation studies are conducted to compare the finite sample performances of the kernel neighbourhood smoothing and the single nearest neighbour smoothing and to check the empirical sizes and powers of the proposed testing procedures. An application to a data set from an AIDS clinical trial study is provided for illustration.     

Perfect samplers for mixtures of distributions

Summary. We consider the construction of perfect samplers for posterior distributions associated with mixtures of exponential families and conjugate priors, starting with a perfect slice sampler in the spirit of Mira and co-workers. The methods rely on a marginalization akin to Rao–Blackwellization and illustrate the duality principle of Diebolt and Robert. A first approximation embeds the finite support distribution on the latent variables within a continuous support distribution that is easier to simulate by slice sampling, but we later demonstrate that the approximation can be very poor. We conclude by showing that an alternative perfect sampler based on a single backward chain can be constructed. This alternative can handle much larger sample sizes than the slice sampler first proposed.     

Ancestral Inference in Population Genetics Models with Selection (with Discussion)

A new algorithm is presented for exact simulation from the conditional distribution of the genealogical history of a sample, given the composition of the sample, for population genetics models with general diploid selection. The method applies to the usual diffusion approximation of evolution at a single locus, in a randomly mating population of constant size, for mutation models in which the distribution of the type of a mutant does not depend on the type of the progenitor allele; this includes any model with only two alleles. The new method is applied to ancestral inference for the two‐allele case, both with genic selection and heterozygote advantage and disadvantage, where one of the alleles is assumed to have resulted from a unique mutation event. The paper describes how the method could be used for inference when data are also available at neutral markers linked to the locus under selection. It also informally describes and constructs the non‐neutral Fleming–Viot measure‐valued diffusion.     

Quality Control Chart for the Mean using Double Ranked Set Sampling

In this paper, an attempt is made to develop Quality Control Charts for monitoring the process mean based on Double Ranked Set Sampling (DRSS) rather than the traditional Simple Random Sampling (SRS). Considering a normal population and several shift values, the performance of the Average Run Length (ARL) of these new charts was compared with the control charts based on Ranked Set Sampling (RSS) and SRS with the same number of observations. It is shown that the new charts do a better job of detecting changes in process mean compared with SRS and RSS.     

ANOMALIES, PROBINGS, INSIGHTS: KEN FOREMAN'S ROLE IN THE SAMPLING INFERENCE CONTROVERSY OF THE LATE 20TH CENTURY

This paper is based on the author's recollections of work done for and with E.K. Foreman, and later developments of that work. It describes most particularly the author's early intimations of the potential for using prediction models in survey sampling, the reasons why the use of such models, especially for inferential purposes, was so strongly resisted in the second half of the 20th century, the manner in which randomization and prediction inferences can be combined, and some advantages flowing from that combination.     

DOMAIN ESTIMATION IN FINITE POPULATIONS1

This paper suggests unbiased estimators (UE's) for the size, mean and total of a domain, with specific features, in a given finite population on the basis of simple random sampling without replacement (SRSWOR) continued till a preassigned number of domain members is observed.