Generalized sequential ranks and tests of randomness

Generalized sequential ranks are defined and are proved to be independent and uniformly distributed under the hypothesis of randomness. By comparison with a Spear-MAsr-type statistic it is shown that in certain cases the test based on the sum of all sequential ranks is an asymptotically optimum test for trend against logistic regression. The test is equivalent to tests proposed by Jonckheere and Terpstra and has a high efficiency when compared with the optimal parametric test for normal regression alternatives.     

Estimation in long memory time series models

A regression type estimator of the parameter d in fractionally differenced ARMA (p,q) processes is presented. The proposed estimator is shown to be mean square consistent. Its performance is compared with some of the existing estimators via a simulation study.     

略论蜀汉政权的选举制度

三国时期,刘备建立的蜀汉政权国祚最短,故在制度创新方面,建树不多。关于蜀国的政治和经济制度,陈寿《三国志》记载粗略,其他文献亦语焉未祥,这对于还原蜀汉政权的制度建设,造成相当大的困难。以下就蜀汉政权制度建设中的选举制度及其特点进行讨论,指出蜀汉政权并未实行如曹魏、孙吴所使用的较成熟的九品官人法之深层原因。     

Weibull inference using trimmed samples and prior information

Trimmed samples are commonly used in several branches of statistical methodology, especially when the presence of contaminated data is suspected. Assuming that certain proportions of the smallest and largest observations from a Weibull sample are unknown or have been eliminated, a Bayesian approach to point and interval estimation of the scale parameter, as well as hypothesis testing and prediction, is presented. In many cases, the use of substantial prior information can significantly increase the quality of the inferences and reduce the amount of testing required. Some Bayes estimators and predictors are derived in closed-forms. Highest posterior density estimators and credibility intervals can be computed using iterative methods. Bayes rules for testing one- and two-sided hypotheses are also provided. An illustrative numerical example is included.     

Target estimation for the logistic regression model

The method of target estimation developed by Cabrera and Fernholz [(1999). Target estimation for bias and mean square error reduction. The Annals of Statistics, 27(3), 1080–1104.] to reduce bias and variance is applied to logistic regression models of several parameters. The expectation functions of the maximum likelihood estimators for the coefficients in the logistic regression models of one and two parameters are analyzed and simulations are given to show a reduction in both bias and variability after targeting the maximum likelihood estimators. In addition to bias and variance reduction, it is found that targeting can also correct the skewness of the original statistic. An example based on real data is given to show the advantage of using target estimators for obtaining better confidence intervals of the corresponding parameters. The notion of the target median is also presented with some applications to the logistic models.     

Estimating Merging Costs by Merger Preconditions

This article provides a method for estimating the bounds of transaction costs in horizontal mergers. Consider, for example, a completed monopoly merger in linear Cournot oligopolies with 10 symmetric firms. The method shows that its transaction costs are at most 25% (78%) of total premerger profits if there is zero (100%) excess capacity. Such estimations can be extended in a straightforward manner to other mergers and other oligopoly models. The estimation is based both on the profitability precondition, and on the non-empty core precondition, which postulates that the split of a merger’s profits be in its core. The article shows that the core in linear Cournot oligopolies has a non-empty interior, and indicates that the non-empty core precondition also sheds new lights on understanding important issues such as the stylized fact that mergers are likely to occur in markets plagued by excess capacities; why profitable mergers might not be formed; and why completed mergers might break up in the future.      

Parameter estimation in semi-linear models using a maximal invariant likelihood function

In this paper, we consider the problem of estimation of semi-linear regression models. Using invariance arguments, Bhowmik and King [2007. Maximal invariant likelihood based testing of semi-linear models. Statist. Papers 48, 357–383] derived the probability density function of the maximal invariant statistic for the non-linear component of these models. Using this density function as a likelihood function allows us to estimate these models in a two-step process. First the non-linear component parameters are estimated by maximising the maximal invariant likelihood function. Then the non-linear component, with the parameter values replaced by estimates, is treated as a regressor and ordinary least squares is used to estimate the remaining parameters. We report the results of a simulation study conducted to compare the accuracy of this approach with full maximum likelihood and maximum profile-marginal likelihood estimation. We find maximising the maximal invariant likelihood function typically results in less biased and lower variance estimates than those from full maximum likelihood.     

A representation in beta series for the exact density of some random volume contents

Consider r independent and identically distributed random points in a unit n-ball of which p are in the interior and rp are on the surface. These r points, via their convex hull, generate an r-simplex. This article deals with the exact density of the r-content when the points are uniformly distributed. The exact density of the r-content is obtained for the general values of the parameters r, n and p. A representation of the density is given as a mixture of beta type-1 densities so that one can evaluate various types of probabilities by using incom-plete beta tables.     

Applications of asymptotic confidence intervals with continuity corrections for asymmetric comparisons in noninferiority trials

A large‐sample problem of illustrating noninferiority of an experimental treatment over a referent treatment for binary outcomes is considered. The methods of illustrating noninferiority involve constructing the lower two‐sided confidence bound for the difference between binomial proportions corresponding to the experimental and referent treatments and comparing it with the negative value of the noninferiority margin. The three considered methods, Anbar, Falk–Koch, and Reduced Falk–Koch, handle the comparison in an asymmetric way, that is, only the referent proportion out of the two, experimental and referent, is directly involved in the expression for the variance of the difference between two sample proportions. Five continuity corrections (including zero) are considered with respect to each approach. The key properties of the corresponding methods are evaluated via simulations. First, the uncorrected two‐sided confidence intervals can, potentially, have smaller coverage probability than the nominal level even for moderately large sample sizes, for example, 150 per group. Next, the 15 testing methods are discussed in terms of their Type I error rate and power. In the settings with a relatively small referent proportion (about 0.4 or smaller), the Anbar approach with Yates’ continuity correction is recommended for balanced designs and the Falk–Koch method with Yates’ correction is recommended for unbalanced designs. For relatively moderate (about 0.6) and large (about 0.8 or greater) referent proportion, the uncorrected Reduced Falk–Koch method is recommended, although in this case, all methods tend to be over‐conservative. These results are expected to be used in the design stage of a noninferiority study when asymmetric comparisons are envisioned. Copyright © 2013 John Wiley & Sons, Ltd.     

城市岩溶区地铁隧道的溶洞超前探测及处治技术

以正在施工的大连地铁2号线（松江路站～东纬路站）暗挖区间工程为例，介绍了暗挖爆破法穿越富水岩溶区、溶洞发育区域时的施工工序流程和超前地质预报手段。利用地质补勘钻孔、超高密度电法跨孔电阻率CT探测、洞内超前探孔等技术手段详细探明溶洞发育位置、形态，通过洞内与地表相结合的处理方式消除或减小溶洞对暗挖施工的影响。超前地质预报手段与施工工序流程的成功应用，为类似环境下城市地铁施工提供参考及借鉴意义。