A note on the bias and consistency of the jackknife variance estimator in stratified samples

Using the ANOVA decomposition, we obtain an explicit formula for the bias of the jackknife variance estimator in stratified samples drawn without replacement. For a wide class of asymptotically linear statistics, we show the consistency of the jackknife variance estimator and establish the asymptotic normality of their Studentized versions.     

General Saddlepoint Approximation for Testing Separate Location-Scale Families of Hypotheses

For testing separate families of hypotheses, the likelihood ratio test does not have the usual asymptotic properties. This paper considers the asymptotic distribution of the ratio of maximized likelihoods (RML) statistic in the special case of testing separate scale or location-scale families of distributions. We derive saddlepoint approximations to the density and tail probabilities of the log of the RML statistic. These approximations are based on the expansion of the log of the RML statistic up to the second order, which is shown not to depend on the location and scale parameters. The resulting approximations are applied in several cases, including normal versus Laplace, normal versus Cauchy, and Weibull versus log-normal. Our results show that the saddlepoint approximations are satisfactory, even for fairly small sample sizes, and are more accurate than normal approximations and Edgeworth approximations, especially for tail probabilities that are the values of main interest in hypothesis testing problems.     

On Power Approximations and Comparison of Several Asymptotic Tests to Detect a Specified Difference between Two Proportions

A large sample test is proposed for a problem of testing for a specified difference between two binomial proportions. The test is compared to the tests by Falk and Koch (1998 Falk , R. W. , Koch , G. G. ( 1998 ). Testing a specified difference between proportions . Biometrics 54 ( 4 ): 1602 – 1614 .[Crossref] , [Google Scholar]), and Parmet and Schechtman (2007 Parmet , Y. , Schechtman , E. ( 2007 ). On a test of the difference between two binomial proportions . Communications in Statistics – Theory and Methods 36 : 887 – 895 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and is shown to dominate in terms of the Type I error rate control. Asymptotic power is derived for each test and is shown to result in values quite proximate to the simulated power values. In addition, formulas to perform sample size estimation are provided. These methods are expected to be especially valuable in the design stage when obtaining the correct power/sample size estimation is essential.     

当前经济发展面临的新形势和新任务

本文基于国际经济仍处于国际金融危机后深度调整期、国内经济步入新常态发展期的新形势,从发展、改革、结构调整、民生改善、防范经济和金融风险的角度,深入分析了当前经济发展面临的新任务,指出促进经济发展应树立的空间思维、历史思维、法治思维和专业思维,以准确把握未来经济发展方向。     

Normal probability plots with confidence for the residuals in linear regression

Normal probability plots for a simple random sample and normal probability plots for residuals from linear regression are not treated differently in statistical text books. In the statistical literature, 1 ? α simultaneous probability intervals for augmenting a normal probability plot for a simple random sample are available. The first purpose of this article is to demonstrate that the tests associated with the 1 ? α simultaneous probability intervals for a simple random sample may have a size substantially different from α when applied to the residuals from linear regression. This leads to the second purpose of this article: construction of four normal probability plot-based tests for residuals, which have size α exactly. We then compare the powers of these four graphical tests and a non-graphical test for residuals in order to assess the power performances of the graphical tests and to identify the ones that have better power. Finally, an example is provided to illustrate the methods.     

Topp–Leone normal distribution with application to increasing failure rate data

In this article, we proposed a new three-parameter probability distribution, called Topp–Leone normal, for modelling increasing failure rate data. The distribution is obtained by using Topp–Leone-X family of distributions with normal as a baseline model. The basic properties including moments, quantile function, stochastic ordering and order statistics are derived here. The estimation of unknown parameters is approached by the method of maximum likelihood, least squares, weighted least squares and maximum product spacings. An extensive simulation study is carried out to compare the long-run performance of the estimators. Applicability of the distribution is illustrated by means of three real data analyses over existing distributions.     

Asymptotic linearity and limit distributions,approximations

Linear and quadratic forms as well as other low degree polynomials play an important role in statistical inference. Asymptotic results and limit distributions are obtained for a class of statistics depending on μ+X$\mu +\mathbf{X}$, with X any random vector and μ$\mu$ non-random vector with ∥μ∥→+∞$\parallel \mu \parallel \to +\infty$. This class contain the polynomials in μ+X$\mu +\mathbf{X}$. An application to the case of normal X is presented. This application includes a new central limit theorem which is connected with the increase of non-centrality for samples of fixed size. Moreover upper bounds for the suprema of the differences between exact and approximate distributions and their quantiles are obtained.     

Approximations to the distribution of weighted combination of independent probabilities

Two simple approximations are proposed for the distribution of the weighted combina-tion of n independent probabilities. The approximations are compared with other avail-able approximations. It is shown that one of the proposed approximations is better than the other approximations.     

职技高师院校特困生问题的探索与对策

随着高校招生及收费制度的改革,高校中逐步出现了“特困生”这一特殊群体。特困生是高校教育改革中出现的一个新问题,受到了党和政府、社会、学校的广泛关注。为了深入细致地做好职技高师院校特困生的教育管理工作,对特困生的形成原因进行了分析,从特困生存在的问题出发,经过深入地探索和思考,总结出了解决职技高师特困生问题的对策。     

论美国新政"常平仓计划"受王安石经济思想的影响--兼与卜德先生商榷

通过史实的发掘和比较发现 ,大萧条期间华莱士执行的“常平仓计划”的思想原型是王安石变法的青苗法和市易法 ,当时的商品信贷公司和剩余商品救济公司就是根据青苗法和市易法建立的。由此证明 ,卜德认为“常平仓计划”与王安石变法无关的看法是错误的。