Estimating Average Worth of the Selected Subset from Two-Parameter Exponential Populations

ABSTRACT

Suppose independent random samples are available from k(k ≥ 2) exponential populations ∏₁,…,∏ _k with a common location θ and scale parameters σ₁,…,σ _k , respectively. Let X _i and Y _i denote the minimum and the mean, respectively, of the ith sample, and further let X = min{X ₁,…, X _k } and T _i  = Y _i  ? X; i = 1,…, k. For selecting a nonempty subset of {∏₁,…,∏ _k } containing the best population (the one associated with max{σ₁,…,σ _k }), we use the decision rule which selects ∏ _i if T _i  ≥ c max{T ₁,…,T _k }, i = 1,…, k. Here 0 < c ≤ 1 is chosen so that the probability of including the best population in the selected subset is at least P* (1/k ≤ P* < 1), a pre-assigned level. The problem is to estimate the average worth W of the selected subset, the arithmetic average of means of selected populations. In this article, we derive the uniformly minimum variance unbiased estimator (UMVUE) of W. The bias and risk function of the UMVUE are compared numerically with those of analogs of the best affine equivariant estimator (BAEE) and the maximum likelihood estimator (MLE).     

Bayesian Estimation of the Size of a Closed Population Using Photo-ID Data with Part of the Population Uncatchable

Abstract

We develop a Bayesian statistical model for estimating bowhead whale population size from photo-identification data when most of the population is uncatchable. The proposed conditional likelihood function is a product of Darroch's model, formulated as a function of the number of good photos, and a binomial distribution of captured whales given the total number of good photos at each occasion. The full Bayesian model is implemented via adaptive rejection sampling for log concave densities. We apply the model to data from 1985 and 1986 bowhead whale photographic studies and the results compare favorably with the ones obtained in the literature. Also, a comparison with the maximum likelihood procedure with bootstrap simulation is considered using different vague priors for the capture probabilities.     

Blinded sample size re-estimation in clinical trials comparing several treatments

An important question that arises in clinical trials is how many additional observations, if any, are required beyond those originally planned. This has satisfactorily been answered in the case of two-treatment double-blind clinical experiments. However, one may be interested in comparing a new treatment with its competitors, which may be more than one. This problem is addressed in this investigation involving responses from arbitrary distributions, in which the mean and the variance are not functionally related. First, a solution in determining the initial sample size for specified level of significance and power at a specified alternative is obtained. Then it is shown that when the initial sample size is large, the nominal level of significance and the power at the pre-specified alternative are fairly robust for the proposed sample size re-estimation procedure. An application of the results is made to the blood coagulation functionality problem considered by Kropf et al. [Multiple comparisons of treatments with stable multivariate tests in a two-stage adaptive design, including a test for non-inferiority, Biom. J. 42(8) (2000), pp. 951–965].     

Testing Variability in the Two-Sample Case

A number of robust methods for testing variability have been reported in previous literature. An examination of these procedures for a wide variety of populations confirms their general robustness. Shoemaker's improvement of the F test extends that test use to a realistic variety of population shapes. However, a combination of the Brown–Forsythe and O'Brien methods based on testing kurtosis is shown to be conservative for a wide range of sample sizes and population distributions. The composite test is also shown to be more powerful in most conditions than other conservative procedures.     

中山国婚制、婚俗初探

中山国由于处于华夏族文化圈内的地理环境和游牧民族逐水草而迁徒的生产、生活方式,因此,它既接受了华夏族国家普遍实行的嫡庶妻婚制,又保留了本民族游徙而嫁的婚俗,还受到境内商族遗民男女无别遗风的熏染,从而使中山国的婚姻形态呈现出诸民族融合的多元化色彩。     

The simultaneous confidence intervals for all distances from the extreme populations for two-parameter exponential populations based on the multiply type II censored samples

Among k independent two-parameter exponential distributions which have the common scale parameter, the lower extreme population (LEP) is the one with the smallest location parameter and the upper extreme population (UEP) is the one with the largest location parameter. Given a multiply type II censored sample from each of these k independent two-parameter exponential distributions, 14 estimators for the unknown location parameters and the common unknown scale parameter are considered. Fourteen simultaneous confidence intervals (SCIs) for all distances from the extreme populations (UEP and LEP) and from the UEP from these k independent exponential distributions under the multiply type II censoring are proposed. The critical values are obtained by the Monte Carlo method. The optimal SCIs among 14 methods are identified based on the criteria of minimum confidence length for various censoring schemes. The subset selection procedures of extreme populations are also proposed and two numerical examples are given for illustration.     

关于“一房多卖”的法律问题探析

近年来,我国的商品房和二手房交易市场日趋活跃,但随之而来的大量商品房买卖纠纷也逐渐成为社会关注的焦点,"一房多卖"便是焦点之一。对各种情形下房屋的所有权归属和法律责任等相关问题进行简要分析,并对登记的效力、优先权等相关问题进行探索具有重要意义。     

一类标签细胞种群系统的适定性与稳定性

研究一类标签细胞系统的解,使用泛函分析方法,特别是Banach 上的线性算子理论和半群理论,证明了该系统解的适定性、线性稳定性和指数稳定性.     

Person-oriented research ethics: integrating relational and everyday ethics in research

Research ethics is often understood by researchers primarily through the regulatory framework reflected in the research ethics review process. This regulatory understanding does not encompass the range of ethical considerations in research, notably those associated with the relational and everyday aspects of human subject research. In order to support researchers in their effort to adopt a broader lens, this article presents a “person-oriented research ethics” approach. Five practical guideposts of person-oriented research ethics are identified, as follows: (1) respect for holistic personhood; (2) acknowledgement of lived world; (3) individualization; (4) focus on researcher-participant relationships; and (5) empowerment in decision-making. These guideposts are defined and illustrated with respect to different aspects of the research process (e.g., research design, recruitment, data collection). The person-oriented research ethics approach provides a toolkit to individual researchers, research groups, and research institutions in both biomedical and social science research wishing to expand their commitment to ethics in research.