Sequential Comparison of d Populations and Related Tables

The paper deals with the numerical solution of the likelihood equations for incomplete data from exponential families, that is for data being a function of exponential family data. Illustrative examples especially studied in this paper concern grouped and censored normal samples and normal mixtures. A simple iterative method of solution is proposed and studied. It is shown that the sequence of iterates converges to a relative maximum of the likelihood function, and that the convergence is geometric with a factor of convergence which for large samples equals the maxi-mal relative loss of Fisher information due to the incompleteness of data. This large sample factor of convergence is illustrated diagrammaticaily for the examples mentioned above. Experiences of practical application are mentioned.     

An Efficient Method to Generate Data and Compute Exact P-Values in Goodness-of-Fit Testing

In this article, we use a characterization of the set of sample counts that do not match with the null hypothesis of the test of goodness of fit. Two direct applications arise: first, to instantaneously generate data sets whose corresponding asymptotic P-values belong to a certain pre-defined range; and second, to compute exact P-values for this test in an efficient way. We present both issues before illustrating them by analyzing a couple of data sets. Method's efficiency is also assessed by means of simulations. We focus on Pearson's X ² statistic but the case of likelihood-ratio statistic is also discussed.     

A Comparison of Some Tests for Determining the Number of Nonzero Canonical Correlations

When considering the relationships between two sets of variates, the number of nonzero population canonical correlations may be called the dimensionality. In the literature, several tests for dimensionality in the canonical correlation analysis are known. A comparison of seven sequential test procedures is presented, using results from some simulation study. The tests are compared with regard to the relative frequencies of underestimation, correct estimation, and overestimation of the true dimensionality. Some conclusions from the simulation results are drawn.     

Confidence Interval of the Difference of Two Independent Binomial Proportions Using Weighted Profile Likelihood

Interval estimation of the difference of two independent binomial proportions is an important problem in many applied settings. Newcombe (1998 Newcombe , R. G. ( 1998 ). Interval estimation for the difference between independent proportions: comparison of seven methods . Statistics in Medicine 17 : 873 – 890 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) compared the performance of several existing asymptotic methods, and based on the results obtained, recommended a method known as Wilson's method, a modified version of a method originally proposed for single binomial proportion. In this article, we propose a method based on profile likelihood, where the likelihood is weighted by noninformative Jeffrey' prior. By doing extensive simulations, we find that the proposed method performs well compared to Wilson's method. A SAS/IML program implementing this method is also given with this article.     

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.