A truncated Cramér–von Mises test of normality

A new test of normality with unknown parameters is proposed in this article. We introduce a Cramér–von Mises type statistic with weight function equal to the inverse of the standard normal density function supported in the interval ript>rc="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/lsta20/2019/lsta20.v048.i16/03610926.2018.1465093/20190701/images/lsta_a_1465093_ilm0001.gif"}' />ript>rc="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/lsta20/2019/lsta20.v048.i16/03610926.2018.1465093/20190701/images/lsta_a_1465093_ilm0001.gif"}" />rc="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />roll" altimg="eq-00001.gif">row>retchy="false">[?row>arow>n,row>arow>nretchy="false">]row> depending on the sample size n. The sequence ript>rc="//:0" data-src='{"type":"image","src":"/na101/home/literatum/publisher/tandf/journals/content/lsta20/2019/lsta20.v048.i16/03610926.2018.1465093/20190701/images/lsta_a_1465093_ilm0002.gif"}' />ript>rc="//:0" alt="" class="mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/lsta20/2019/lsta20.v048.i16/03610926.2018.1465093/20190701/images/lsta_a_1465093_ilm0002.gif"}" />rc="//:0" alt="" data-formula-source="{"type" : "mathjax"}" />roll" altimg="eq-00002.gif">row>{row>arow>n}row> is chosen so that the statistic goes to infinity and after subtracting the mean, a suitable test statistic is obtained, with the same asymptotic law as the well-known Shapiro–Wilk statistic. It is shown that the performance of the new test in many cases improves that of other well-known tests of normality.     

Any complete preference structure without circuit admits an interval representation

This article proves that all complete preference structures where the strict preference relation (P) has no circuit admit a representation by intervals of the real line; the rule for deciding whether an interval is indifferent or preferred to another is less straightforward than for interval orders: strict preference is indeed compatible with a certain degree of overlapping of intervals, the allowed degree being specified by means of a so-called tolerance function.     

初等r-循环矩阵的几个性质

给出了初等ｒ－循环矩阵可逆的充要条件及逆矩阵的表达式;对奇异的初等ｒ－循环矩阵给出了Ａ的一个ｇ－逆Ｇ（满足ＡＧＡ＝Ａ,ＧＡＧ＝Ｇ）及Ｍｏｏｒｅ－ｐｅｎｒｏｓｅ广义逆矩阵的表达式．     

从saragur到salr——撒拉族源流的语言人类学研究

本文以撒拉族相关族名为重点,通过语言人类学的研究,提出撒拉族源自Qaramang(尕勒莽)部,和土库曼、土耳其的Karaman,乌兹别克的努尔塔Salur人都应是源自历史上著名的、Salur乌古斯部的一位领袖Karaman的观点。撒拉族的自称Salr,是由历史上的Salur、Salgur、*Saragur、*Sarg Ogur等演变而来。Sarg Ogur意为"黄箭(部落)",曾是匈奴的一个重要组成部分。撒拉族等一些乌古斯(Ouz)民族和维吾尔族、裕固族的祖先回纥(Ogur)都同出一源。     

r型槽与螺旋槽干式气体密封性能对比研究

为了改善螺旋槽干式气体端面密封性能,提出了一种由螺旋槽和圆弧槽组合的r型槽干式气体密封,并根据气体润滑理论建立了r型槽干式气体密封数值分析模型,定义了r型槽的主要几何结构参数,采用有限元方法求解雷诺方程,获得了端面气膜压力分布,分析了转速、压力对端面开启力、泄漏量等密封性能参数的影响规律,并与螺旋槽干式气体密封进行了对比研究。结果表明,r型槽干式气体密封中圆弧槽有回流作用,与螺旋槽干式气体密封相比有较小的泄漏量;r型槽干式气体密封更适用于低压高速场合。     

Testing independence based on Bernstein empirical copula and copula density

In this paper we provide three nonparametric tests of independence between continuous random variables based on the Bernstein copula distribution function and the Bernstein copula density function. The first test is constructed based on a Cramér-von Mises divergence-type functional based on the empirical Bernstein copula process. The two other tests are based on the Bernstein copula density and use Cramér-von Mises and Kullback–Leibler divergence-type functionals, respectively. Furthermore, we study the asymptotic null distribution of each of these test statistics. Finally, we consider a Monte Carlo experiment to investigate the performance of our tests. In particular we examine their size and power which we compare with those of the classical nonparametric tests that are based on the empirical distribution function.     

Cramér–von Mises distance: probabilistic interpretation,confidence intervals,and neighbourhood-of-model validation

We give a probabilistic interpretation of the Cramér–von Mises distance ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0001.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0001.gif"}" /> between continuous distribution functions F and ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0002.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0002.gif"}" />. If F is unknown, we construct an asymptotic confidence interval for ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0003.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0003.gif"}" /> based on a random sample from F. Moreover, for given ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0004.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0004.gif"}" /> and some value ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0005.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0005.gif"}" />, we propose an asymptotic equivalence test of the hypothesis that ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0006.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0006.gif"}" /> against the alternative ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0007.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0007.gif"}" />. If such a ‘neighbourhood-of-ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0008.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0008.gif"}" /> validation test’, carried out at a small asymptotic level, rejects the hypothesis, there is evidence that F is within a distance ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0009.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0009.gif"}" /> of ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0010.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0010.gif"}" />. As a neighbourhood-of-exponentiality test shows, the method may be extended to the case that ript>rc="/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0011.gif" alt=" />ript>rc="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" alt=" class="no-mml-formula" data-formula-source="{"type" : "image", "src" : "/na101/home/literatum/publisher/tandf/journals/content/gnst20/2017/gnst20.v029.i02/10485252.2017.1285029/20170405/images/gnst_a_1285029_ilm0011.gif"}" /> is composite.     

An integral formula for the distribution of self-normalized Gaussian random samples

Given i.i.d. Gaussian random variables and after standardizing the sample by subtracting the sample mean and dividing it by the sample deviation, we obtain an integral formula for the distribution of these self-normalized variables. Using geometrical arguments, we obtain the distribution of each and the joint distribution of two of them. These formulas can be used to calculate the expected value of the particular type of Cramér von Mises statistic to test normality.     

Displacement and local linguistic practices: R‐lessness in post‐Katrina Greater New Orleans

Variable r‐lessness in New Orleans English is a salient linguistic feature tied to local place‐based identity. In this study, I examine rates of r‐lessness in the wake of Hurricane Katrina, which caused large‐scale displacement in the region. Participants come from the linguistically conservative suburb of Chalmette, where r‐lessness is more robust than in New Orleans proper. Participants’ connections to Chalmette were measured in two ways: (1) post‐Katrina location status, i.e. whether participants returned or relocated after the storm; (2) place orientation, captured via an ethnographically informed, multifaceted measure of stance and exposure to places outside of Chalmette. Analysis revealed that place orientation better predicts rates of r‐lessness than post‐Katrina location. I argue that the marked quality of r‐lessness makes it available for identity‐driven use to express a connection to Chalmette. This study demonstrates one way to account for the linguistic implications of individuals’ shifting allegiances to places they live(d).     

Four Correlation Coefficients with a Third Blocking Variable: Their Efficacy,Relative Efficiency,and Test Statistics

Abstract

The efficacy and the asymptotic relative efficiency (ARE) of a weighted sum of Kendall's taus, a weighted sum of Spearman's rhos, a weighted sum of Pearson's r's, and a weighted sum of z-transformation of the Fisher–Yates correlation coefficients, in the presence of a blocking variable, are discussed. The method of selecting the weighting constants that maximize the efficacy of these four correlation coefficients is proposed. The estimate, test statistics and confidence interval of the four correlation coefficients with weights are also developed. To compare the small-sample properties of the four tests, a simulation study is performed. The theoretical and simulated results all prefer the weighted sum of the Pearson correlation coefficients with the optimal weights, as well as the weighted sum of z-transformation of the Fisher–Yates correlation coefficients with the optimal weights.