Likelihood Ratio Tests for the Non Equivalence of Means

We derive likelihood ratio (LR) tests for the null hypothesis of equivalence that the normal means fall into a practical indifference zone. The LR test can easily be constructed and applied to k ≥ 2 treatments. Simulation results indicate that the LR test might be slightly anticonservative statistically, but when the sample sizes are large, it always produces the nominal level for mean configurations under the null hypothesis. More powerful than the studentized range test, the LR test is a straightforward application that requires only current existing statistical tables, with no complicated computations.     

Distribution-Free Exceedance CUSUM Control Charts for Location

Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. A Phase II nonparametric cumulative sum (CUSUM) chart based on the exceedance statistics, called the exceedance CUSUM chart, is proposed here for detecting a shift in the unknown location parameter of a continuous distribution. The exceedance statistics can be more efficient than rank-based methods when the underlying distribution is heavy-tailed and/or right-skewed, which may be the case in some applications, particularly with certain lifetime data. Moreover, exceedance statistics can save testing time and resources as they can be applied as soon as a certain order statistic of the reference sample is available. Guidelines and recommendations are provided for the chart's design parameters along with an illustrative example. The in- and out-of-control performances of the chart are studied through extensive simulations on the basis of the average run-length (ARL), the standard deviation of run-length (SDRL), the median run-length (MDRL), and some percentiles of run-length. Further, a comparison with a number of existing control charts, including the parametric CUSUM chart and a recent nonparametric CUSUM chart based on the Wilcoxon rank-sum statistic, called the rank-sum CUSUM chart, is made. It is seen that the exceedance CUSUM chart performs well in many cases and thus can be a useful alternative chart in practice. A summary and some concluding remarks are given.     

中国水产品统计数据修正规律研究——以水产品总量和海水产品产量为例

近年来,水产品统计数据存在水分问题引起了广泛关注。国家统计局已对1997—2006年间水产品部分指标数据进行了修正,但未对这些指标的虚报特征进行阐述。通过对修正前后水产品总量和海水产品产量2个指标的数据特征进行分析,发现这2个指标的虚报量存在3点规律:2个指标的虚报量变化规律均符合带截距线性模型;2个变量的估计虚报量可以分解为固定虚报量和可变虚报量两部分;从增长率、固定虚报量、可变虚报量变化率和平均虚报率角度来看,水产品总量虚报特征均强于海水产品虚报特征。     

A HEWMA-CUSUM control chart for the Weibull distribution

The Weibull distribution is one of the most popular distributions for lifetime modeling. However, there has not been much research on control charts for a Weibull distribution. Shewhart control is known to be inefficient to detect a small shift in the process, while exponentially weighted moving average (EWMA) and cumulative sum control chart (CUSUM) charts have the ability to detect small changes in the process. To enhance the performance of a control chart for a Weibull distribution, we introduce a new control chart based on hybrid EWMA and CUSUM statistic, called the HEWMA-CUSUM chart. The performance of the proposed chart is compared with the existing chart in terms of the average run length (ARL). The proposed chart is found to be more sensitive than the existing chart in ARL. A simulation study is provided for illustration purposes. A real data is also applied to the proposed chart for practical use.     

The power piecewise exponential model

In this paper an extension of the piecewise exponential distribution based on the distribution of the maximum of a random sample is considered. Properties of its density and hazard function are investigated. Maximum likelihood inference is discussed and the Fisher information matrix is identified. Results of two real data applications are reported, where model fitting is implemented by using maximum likelihood. The applications illustrate the better performance of the new distribution when compared with other recently proposed alternative models.     

LIMIT THEOREMS FOR PROPORTIONS OF OBSERVATIONS FALLING INTO RANDOM REGIONS DETERMINED BY ORDER STATISTICS

In this paper, we study asymptotic behavior of proportions of sample observations that fall into random regions determined by a given Borel set and an order statistic. We show that these proportions converge almost surely to some population quantities as the sample size increases to infinity. We derive our results for independent and identically distributed observations from an arbitrary cumulative distribution function, in particular, we allow samples drawn from discontinuous laws. We also give extensions of these results to the case of randomly indexed samples with some dependence between observations.     

中美贸易摩擦的认识误区和正解

为了全面理解中美贸易关系,解读中美贸易失衡的本质,从美方特别是特朗普当局如何看待中美贸易失衡入手,通过对中美贸易数据的研判,预测未来中美贸易发展走向。研究发现,特朗普当局认为中国政府对出口企业的补贴以及高关税政策,是中美贸易逆差的主要原因,导致美国制造业丢失了近300万个工作岗位,因此需要打压中国出口,对中国出口到美国的产品征收高关税来扭转贸易逆差,让中国长期处在全球贸易价值链的中低端。研究认为,美国对中美贸易额的统计口径过于简单,减少中国进口不能直接增加美国的就业人数,中国扩大出口能为美国提供“价优物美”产品,中国投资者又把贸易所得投资到美国购买国债,美国是贸易逆差的受益方;中国的大量贸易顺差是劳动密集型产品所得,在资本密集型产品中主要是把中间品加工成最终产品,贸易所得很小;此外,中国的关税政策符合WTO规则,美国也会以“国家安全”为由限制投资。因此,中国从全球贸易价值链的低端爬到中高端是经济发展的必然结果,中美应通过贸易谈判,争取经贸合作,才能够提高双方经贸规模,实现中美贸易朝着合理的方向再平衡。     

对中国大学生英语阅读理解中母语与外语“语言-思维双元结构”相互作用的统计分析

本文在双元结构这一理论假设的指导下,探索语言和思维的相互作用在中国大学生英语阅读理解中的体现,并通过实验,从统计学的角度分析母语和外语的相互参与强度。结果表明:汉语在大学生英语阅读过程中不但有直接影响,而且还通过影响英语语言水平对其施加间接影响;学生利用母语的语言和思维更好地通达外语的意识和能力还有待提高。     

Kernel estimators for the second order parameter in extreme value statistics

We develop and study in the framework of Pareto-type distributions a general class of kernel estimators for the second order parameter ρ$\rho$, a parameter related to the rate of convergence of a sequence of linearly normalized maximum values towards its limit. Inspired by the kernel goodness-of-fit statistics introduced in Goegebeur et al. (2008), for which the mean of the normal limiting distribution is a function of ρ$\rho$, we construct estimators for ρ$\rho$ using ratios of ratios of differences of such goodness-of-fit statistics, involving different kernel functions as well as power transformations. The consistency of this class of ρ$\rho$ estimators is established under some mild regularity conditions on the kernel function, a second order condition on the tail function 1−F of the underlying model, and for suitably chosen intermediate order statistics. Asymptotic normality is achieved under a further condition on the tail function, the so-called third order condition. Two specific examples of kernel statistics are studied in greater depth, and their asymptotic behavior illustrated numerically. The finite sample properties are examined by means of a simulation study.     

Book Reviews

The Levene test is a widely used test for detecting differences in dispersion. The modified Levene transformation using sample medians is considered in this article. After Levene's transformation the data are not normally distributed, hence, nonparametric tests may be useful. As the Wilcoxon rank sum test applied to the transformed data cannot control the type I error rate for asymmetric distributions, a permutation test based on reallocations of the original observations rather than the absolute deviations was investigated. Levene's transformation is then only an intermediate step to compute the test statistic. Such a Levene test, however, cannot control the type I error rate when the Wilcoxon statistic is used; with the Fisher–Pitman permutation test it can be extremely conservative. The Fisher–Pitman test based on reallocations of the transformed data seems to be the only acceptable nonparametric test. Simulation results indicate that this test is on average more powerful than applying the t test after Levene's transformation, even when the t test is improved by the deletion of structural zeros.