Some theoretical results concerning non parametric estimation by using a judgment poststratification sample

ABSTRACT

In this paper, some of the properties of non parametric estimation of the expectation of g(X) (any function of X), by using a judgment poststratification sample (JPS), have been discussed. A class of estimators (including the standard JPS estimator and a JPS estimator proposed by Frey and Feeman (2012 Frey, J., Feeman, T.G. (2012). An improved mean estimator for judgment post-stratification. Comput. Stat. Data Anal. 56(2):418–426.[Crossref], [Web of Science ®] , [Google Scholar], Comput. Stat. Data An.) is considered. The paper provides mean and variance of the members of this class, and examines their consistency and asymptotic distribution. Specifically, the results are for the estimation of population mean, population variance, and cumulative distribution function. We show that any estimators of the class may be less efficient than simple random sampling (SRS) estimator for small sample sizes. We prove that the relative efficiency of some estimators in the class with respect to balanced ranked set sampling (BRSS) estimator tends to 1 as the sample size goes to infinity. Furthermore, the standard JPS mean estimator, and Frey–Feeman JPS mean estimator are specifically studied and we show that two estimators have the same asymptotic distribution. For the standard JPS mean estimator, in perfect ranking situations, optimum values of H (the ranking class size), for different sample sizes, are determined non parametrically for populations that are not heavily skewed or thick tailed.     

Robust and nonparametric subset selection procedures

Subset selection procedures based on ranks have been investigated by a number of authors previously. Their methods are based on ranking the samples from all the populations jointly. However, as was pointed out by Rizvi and Woodworth (1970), the procedures they proposed cannot control the probability of a correct selection over the entire parameter space. In this paper, we propose a subset selection procedure based on pairwise rather than joint ranking of the samples. It is shown that this procedure controls the probability of a correct selection over the entire parameter space. It is also shown that the Pitman efficiency of this nonparametric procedure relative to the multivariate t procedure of Gupta (1956, 1965) is the same as the Pitman efficiency of the Mann-Whitney-Wilcoxon test relative to the t-test.     

Selection of the best in 2×2 factorial designs

Selection of the cell in a 2×2 -factorial design with the greatest mean is considered. A general class of ranking and selection procedures (RSP) is constructed to include methods based on the largest marginal cell means (SP1) or on the largest cell mean (SP3). Using the preference zone approach the minimum probability of a correct solution is found, In this paper a RSP which maximizes the minimum probability of a correct solution over the preference zone is found. In this way selection of the cell with the greatest observed mean is proven to be admissible.     

A predictive approach for the selection of a fixed number of good treatments

This paper offers a predictive approach for the selection of a fixed number (= t) of treatments from k treatments with the goal of controlling for predictive losses. For the ith treatment, independent observations X _ij (j = 1,2,…,n) can be observed where X _ij ’s are normally distributed N(θ _i ; σ ²). The ranked values of θ _i ’s and X _i ’s are θ ₍₁₎ ≤ … ≤ θ _(k) and X _[1] ≤ … ≤ X _[k] and the selected subset S = {[k], [k? 1], … , [k ? t+1]} will be considered. This paper distinguishes between two types of loss functions. A type I loss function associated with a selected subset S is the loss in utility from the selector’s view point and is a function of θ _i with i ? S. A type II loss function associated with S measures the unfairness in the selection from candidates’ viewpoint and is a function of θ _i with i ? S. This paper shows that under mild assumptions on the loss functions S is optimal and provides the necessary formulae for choosing n so that the two types of loss can be controlled individually or simultaneously with a high probability. Predictive bounds for the losses are provided, Numerical examples support the usefulness of the predictive approach over the design of experiment approach.     

高校排名问题及其管理学研究

高校排名,是近年来社会比较关注的一个热点问题,人们对它贬褒不一.由于它操作过程的民间性、自由性与评价结果的影响性与误导作用,引起了众多学者与社会人士的强烈反响,也值得我们各级政府教育管理部门的高度注意.笔者对高校排名问题进行了系统研究,内容包括高校排名问题的提出与界定、国外排名指标与方法综述、当前国内高校排名中的问题分析、以及我们对排名指标及其方法的思考与建议等内容.     

试评中国大学排名榜

通过对大学排名榜引起激烈争辩的原因进行分析,指出其存在三方面的问题:排名失真是各方看法不一的关键;其次,关联各方(中介排名评价方、被评校方和普通公众)对排名榜的认识尚存在诸多误区;最后,校方担心排名榜会影响政府部门对学校的资助力度和考生对学校的选择。分析指出,对高校的评价排名关键在于坚持理性。     

关于我国大学排行评价的几点质疑

对大学办学水平和声誉进行综合性排行评价,是一项复杂的工作。我国的大学排行评价时间短、不成熟,排行结果的合理性和权威性应受质疑。评价理论不完善,评价客体的不可比性和评价主体的主观性,导致了大学排行评价基础的不合理性;评价的数据不全面、不准确,评价的方法不科学、不得当,导致了大学排行评价过程暴露出的破绽比比皆是;缺乏特定大学的完整的质量信息,导致了大学排行评价结果的极大局限性。     

Testing for the Presence of a Maverick Judge

Abstract

The presence of a maverick judge, one whose rankings differ greatly from the other members of a panel, can result in incorrect rankings and a sense of unfairness among contestants. We develop and explore the properties of a likelihood ratio test, assuming a Mallows type distribution, for the presence of a maverick judge when each judge selects his or her best k out of n objects, k ≤ n. Detection of a maverick judge, who may be viewed as a multivariate outlier, turns out to be very difficult unless the judges are very consistent and there are repeat observations on the panel.     

Selection and ranking procedures: a brief introduction

This paper presents a brief introduction to selection and ranking methodology. Both indifference zone and subset selection approaches are discussed along with some modifications and generalizations. Two examples are provided to illustate the use of subset selection and the indifference zone approaches. The paper concludes with the remark that selection and ranking methodology is a realistic approach in statistical analyses involving comparisons among two or more treatments.