Optimal determination of the parameters of some biased estimators using genetic algorithm

In this paper, some new algorithms for estimating the biasing parameters of the ridge, Liu and two-parameter estimators are introduced with the help of genetic algorithm (GA). The proposed algorithms are based on minimizing some statistical measures such as mean square error (MSE), mean absolute error (MAE) and mean absolute prediction error (MAPE). At the same time, the new algorithms allow one to keep the condition number and variance inflation factors to be less than or equal to ten by means of the GA. A numerical example is presented to show the utility of the new algorithms. In addition, an extensive Monte Carlo experiment is conducted. The numerical findings prove that the proposed algorithms enable to eliminate the problem of multicollinearity and minimize the MSE, MAE and MAPE.     

中国—东盟政治合作机制研究

本文根据中国—东盟区域合作发展的政治合作机制的概念及呈现的多维特性,运用政治合作的目标分解和构成要素,对政治合作机制进行综合的结构分析。通过利益泛化(低度)、制度分化(中度)和价值固化(深度)生成的三个阶段性使命目标(和睦共享、和平共处与和谐共荣)合作过程的剖析,对中国—东盟政治合作机制建设的结构性问题进行探讨,以此助推区域政治合作机制的改进和优化。     

A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

ABSTRACT

A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some prespecified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser’s directional two-sided test as well as the more recently introduced testing procedure of Jones and Tukey, each equivalent to running two one-sided tests, involve three possible decisions to infer the value of a unidimensional parameter. The latter procedure assumes that a point null hypothesis is impossible (e.g., that two treatments cannot have exactly the same effect), allowing a gain of statistical power. There are, however, situations where a point hypothesis is indeed plausible, for example, when considering hypotheses derived from Einstein’s theories. In this article, we introduce a five-decision rule testing procedure, equivalent to running a traditional two-sided test in addition to two one-sided tests, which combines the advantages of the testing procedures of Kaiser (no assumption on a point hypothesis being impossible) and Jones and Tukey (higher power), allowing for a nonnegligible (typically 20%) reduction of the sample size needed to reach a given statistical power to get a significant result, compared to the traditional approach.     

考虑储存成本的集装箱公铁联运路径优化

联运企业的效益受运输路径和运输方式的影响。如何降低联运成本、提高联运企业的效益,已成为学术研究的重中之重。针对集装箱公铁联运路径优化问题,以运输成本、换装成本、储存成本、时间惩罚成本构成的运输总成本为目标函数,建立集装箱公铁联运路径优化模型,考虑运输时间限制、班期限制、节点储存成本,得出使运输总成本最低的运输路径及运输方式,并利用算例验证模型的有效性。     

Utilizing Bayesian predictive power in clinical trial design

The Bayesian paradigm provides an ideal platform to update uncertainties and carry them over into the future in the presence of data. Bayesian predictive power (BPP) reflects our belief in the eventual success of a clinical trial to meet its goals. In this paper we derive mathematical expressions for the most common types of outcomes, to make the BPP accessible to practitioners, facilitate fast computations in adaptive trial design simulations that use interim futility monitoring, and propose an organized BPP-based phase II-to-phase III design framework.     

Rare and clustered population estimation using the adaptive cluster sampling with some robust measures

The use of robust measures helps to increase the precision of the estimators, especially for the estimation of extremely skewed distributions. In this article, a generalized ratio estimator is proposed by using some robust measures with single auxiliary variable under the adaptive cluster sampling (ACS) design. We have incorporated tri-mean (TM), mid-range (MR) and Hodges-Lehman (HL) of the auxiliary variable as robust measures together with some conventional measures. The expressions of bias and mean square error (MSE) of the proposed generalized ratio estimator are derived. Two types of numerical study have been conducted using artificial clustered population and real data application to examine the performance of the proposed estimator over the usual mean per unit estimator under simple random sampling (SRS). Related results of the simulation study show that the proposed estimators provide better estimation results on both real and artificial population over the competing estimators.     

A new algorithm for clustering based on kernel density estimation

In this paper, we present an algorithm for clustering based on univariate kernel density estimation, named ClusterKDE. It consists of an iterative procedure that in each step a new cluster is obtained by minimizing a smooth kernel function. Although in our applications we have used the univariate Gaussian kernel, any smooth kernel function can be used. The proposed algorithm has the advantage of not requiring a priori the number of cluster. Furthermore, the ClusterKDE algorithm is very simple, easy to implement, well-defined and stops in a finite number of steps, namely, it always converges independently of the initial point. We also illustrate our findings by numerical experiments which are obtained when our algorithm is implemented in the software Matlab and applied to practical applications. The results indicate that the ClusterKDE algorithm is competitive and fast when compared with the well-known Clusterdata and K-means algorithms, used by Matlab to clustering data.     

Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings

It is known that the normal approximation is applicable for sums of non negative random variables, W, with the commonly employed couplings. In this work, we use the Stein’s method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of W. Applications of the main result to give the bound on normal approximation for binomial random variable, the number of bulbs on at the terminal time in the lightbulb process, and the number of m runs are also provided.     

Business reform outcomes: Why so different?

Post-crisis policy making increasingly focuses on doing business reforms. We argue that the effects of those reforms will be different across countries. To understand the reasons for the reform outcome divergence, we advance a novel firm-size distribution (FSDs) argument. At the center of the argument is the fact that FSDs are different across countries and stable over time. Then, if a given doing business reform induces firms of different size to grow differently, this will produce a variety of reform outcomes across countries. To advance the argument, we set up a tractable general equilibrium (GE) model and study how firms of different size grow after a doing business reform. The model predicts that larger firms will grow faster than smaller firms after the reform. The model predictions are tested on the Enterprise Surveys (ES) data, merged with the Doing Business indicators. We confirm that firms of different size grow differently after a Doing Business reform. Thus, based on the notable differences of firm size distributions across countries, identical reforms to start, operate and close a business will produce a variety of reform outcomes across countries.     

The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.