Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

A modified random-effect procedure for combining risk difference in sets of 2×2 tables from clinical trials

Summary Meta-analyses of sets of clinical trials often combine risk differences from several 2×2 tables according to a random-effects model. The DerSimonian-Laird random-effects procedure, widely used for estimating the populaton mean risk difference, weights the risk difference from each primary study inversely proportional to an estimate of its variance (the sum of the between-study variance and the conditional within-study variance). Because those weights are not independent of the risk differences, however, the procedure sometimes exhibits bias and unnatural behavior. The present paper proposes a modified weighting scheme that uses the unconditional within-study variance to avoid this source of bias. The modified procedure has variance closer to that available from weighting by ideal weights when such weights are known. We studied the modified procedure in extensive simulation experiments using situations whose parameters resemble those of actual studies in medical research. For comparison we also included two unbiased procedures, the unweighted mean and a sample-size-weighted mean; their relative variability depends on the extent of heterogeneity among the primary studies. An example illustrates the application of the procedures to actual data and the differences among the results. This research was supported by Grant HS 05936 from the Agency for Health Care Policy and Research to Harvard University.     

实数域及四元数除环上有平方根的方阵

给出了实数域及实四元数除环上方阵有平方根的充分必要条件．     

Some remarks on the physical models concerning two different approaches to inference in statistical process control

Summary For technological applications it can be useful to identify some simple physical mechanisms, which, on the basis of the available knowledge of the production process, may suggest the most appropriate approach to statistical control of the random quantities of interest. For this purpose the notion of rupture point is introduced firstly. A rupture point is characterized bym randomly arising out of control states, assumed to be mutually exclusive and stochastically independent. Shewhart's control charts seem to represent the natural statistical tool for controlling a rupture point; however it is shown that they are fully justified only when the hazard rates attached to the causes of failure are constant. Otherwise, typically in the presence of time increasing hazard rates, Shewhart's control charts should be completed by a preventive intervention rule (preventive maintenance). In the second place, the notion of dynamic instability point is introduced, which is specifically characterized by assuming that the random quantity of interest is ruled by a stochastic differential equation with constant coefficients. By discretization, developed according to a possibly new approach, it is shown that the former model reduces to an equation error model, which is among the simplest used in adaptive control, and thus particularly easy to deal with in regard to parameter estimation and the definition of the optimum control rule.     

Marginal and association regression models for longitudinal binary data with drop‐outs: A likelihood‐based approach

Longitudinal data often contain missing observations, and it is in general difficult to justify particular missing data mechanisms, whether random or not, that may be hard to distinguish. The authors describe a likelihood‐based approach to estimating both the mean response and association parameters for longitudinal binary data with drop‐outs. They specify marginal and dependence structures as regression models which link the responses to the covariates. They illustrate their approach using a data set from the Waterloo Smoking Prevention Project They also report the results of simulation studies carried out to assess the performance of their technique under various circumstances.     

中国交通运输业发展的实证研究

采用协整和误差纠正模型与方法，对中国改革开放20多年来交通运输发展与一些相关影响因素之间的关系进行实证研究。结果表明：旅客运输需求与国民收入、乘车费用之间，货物运输与国民经济、燃油价格之间分别存在长期稳定关系。研究认为：中国交通的发展应适当超前于国民经济的发展。同时，研究还发现：“旅游黄金周”的实施并不是促进中国旅客运输需求的显著影响因素。     

WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

In this paper, we establish strong laws for weighted sums of negatively associated (NA) random variables which have a higher‐order moment condition. Some results of Bai Z.D. & Cheng P.E. (2000) [Marcinkiewicz strong laws for linear statistics. Statist. and Probab. Lett. 43, 105–112,] and Sung S.K. (2001) [Strong laws for weighted sums of i.i.d. random variables, Statist. and Probab. Lett. 52, 413–419] are sharpened and extended from the independent identically distributed case to the NA setting. Also, one of the results of Li D.L. et al. (1995) [Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab. 8, 49–76,] is complemented and extended.     

Sampling Strategies for Toxic Air Contaminants

Annual concentrations of toxic air contaminants are of primary concern from the perspective of chronic human exposure assessment and risk analysis. Despite recent advances in air quality monitoring technology, resource and technical constraints often impose limitations on the availability of a sufficient number of ambient concentration measurements for performing environmental risk analysis. Therefore, sample size limitations, representativeness of data, and uncertainties in the estimated annual mean concentration must be examined before performing quantitative risk analysis. In this paper, we discuss several factors that need to be considered in designing field-sampling programs for toxic air contaminants and in verifying compliance with environmental regulations. Specifically, we examine the behavior of SO2, TSP, and CO data as surrogates for toxic air contaminants and as examples of point source, area source, and line source-dominated pollutants, respectively, from the standpoint of sampling design. We demonstrate the use of bootstrap resampling method and normal theory in estimating the annual mean concentration and its 95% confidence bounds from limited sampling data, and illustrate the application of operating characteristic (OC) curves to determine optimum sample size and other sampling strategies. We also outline a statistical procedure, based on a one-sided t-test, that utilizes the sampled concentration data for evaluating whether a sampling site is compliance with relevant ambient guideline concentrations for toxic air contaminants.     

BATHTUB-TYPE CURVES IN RELIABILITY AND BEYOND

Finding optimal, or at least good, maintenance and repair policies is crucial in reliability engineering. Likewise, describing life phases of human mortality is important when determining social policy or insurance premiums. In these tasks, one searches for distributions to fit data and then makes inferences about the population(s). In the present paper, we focus on bathtub‐type distributions and provide a view of certain problems, methods and solutions, and a few challenges, that can be encountered in reliability engineering, survival analysis, demography and actuarial science.