A comparison of estimators of the degree of insect control

The current estimator of the degree of insect control by an insecticide in a field experiment laid out in randomized blocks is equal to one minus the cross-product ratio of a two way table of total insect counts over blocks. Since much work has been done on estimation of the common odds ratio of a number of strata in medical studies, a series of Monte Carlo studies was performed to investigate the possible use of these estimators and their standard errors in estimating the common degree of inject control of a number of blocks. Maximum likelihood, Mantel-Haenszel, and empirical logit estimators were evaluated and compared with back-transformed means over blocks, of cross-product ratios on the arithmetic, logarithmic, and arcsine scales. Maximum likelihood and Mantel-Haenszel estimators had the smallest mean squared errors, but their standard error estimates were only appropriate when sampling distributions were approximately Poisson and there was little heterogeneity among plots within blocks in the natural rates of population change.     

Limiting distribution of the number of clumps of palindromes in DNA

An important aspect in the analysis of long DNA sequences is to identify whether palindromes are over- or under-represented. The essential step in that direction is the analysis of the limiting distribution of the number of clumps of palindromes where clump is defined as the overlapping occurrence of palindromes. Using the Chen–Stein method, it is shown in this paper that the limiting distribution, under suitable conditions and a type of heterogeneous sequence, is the Poisson distribution. Moreover, error bounds and the rate of convergence are derived in terms of total variation distance between two probability distributions.     

Test of equality of normal means in the absence of independent estimator of variance

Let X_l,…,X_n be normally and independently distributed with means θ_l,…,θ_nand a cornmorl variance. Thus there are n observations and n+i unknwon parameters. A test of the null hypothesis that, the θ_i's are all zero and the alternative that the vector (θ_l,…,θ_n) lies in a convex cone with its vertex a.t the origin is connsidered in this paper. It is shown that under a mild condition the likelihood ratio test is possible. The ordinary one sided t - test belongs to the class of tests considered in this paper. The hypothesis of equality of means against the simple order alternative can be tested in certain cases .     

三分位数的意义及计算

统计中已有确定中位数、四分位数、十分位数等的方法,文章在此基础上提出三分位数的概念及其确定的方法。三分位数从另一个角度对总体的分布特征进行描绘,对于现象总体的内部构成,对于由不同组成部分、类型形成的总体的认识,对于分组时组间界限的确定,甚至对于分层抽样中层的划分,对于研究分析总体分布的离散程度都有一定的作用。同时对单项式设计的变量数列确定中位数、三分位数的方法也进行了一定的论述。     

History of the Development of Statistics in India

The development of statistics and statistical organization as we know it today, in fact, did not grow in India overnight. It took more than a century to graduate to its present form but its history goes as far back as 300 BC, thus it will be difficult to present in detail in this short article. However, an attempt will be made to study the statistical development in ancient India and throught to the 19th century.     

中国国债融资功能的反思

一、中国国债融资制度的产生在传统计划经济体制下 ,中国的经济资源分配方式是 ,首先由国家强制集中全社会的资本要素 ,然后再用行政手段进行分配。从融资体制角度看 ,国家在这里充当了资本流动的中介 ,国家是融资的主体 ,它把资本从所有者那里筹集起来 ,再分配给他所选择的企业经营者使用 ,这种计划经济下的融资体制被称之为国家融资 (张春霖 ,2 0 0 0 )。在过去的几十年中 ,这种融资体制主要采取了两种基本形式 ,即收入融资和债务融资。所谓收入融资是指国家通过低工资、工农产品剪刀差等途径 ,把城乡居民应得的收入中可以用于长期储蓄的…     

A comparison of estimators of the precision of two instruments

Three different estimators of the variance in errors of measurement, or the “imprecisions” of instruments, have been proposed (Hahn and Nelson, 1970; Maxwell, 1974; Hanumara: 1975) for the case where two measurements by one instrument and one measurement by a second instrument are available for each item. The estimators are compared by studying the probabilities of negative values, the biases, the variances, and the mean square errors. Based on these results, Hahn and Nelson's estimators for the variances in errors of measurement are recommended. Simultaneous confidence intervals of the imprecisions of instruments are also given.     

Parametric estimation of mixtures of two uniform distributions

In this paper, we consider a mixture of two uniform distributions and derive L-moment estimators of its parameters. Three possible ways of mixing two uniforms, namely with neither overlap nor gap, with overlap, and with gap, are studied. The performance of these L-moment estimators in terms of bias and efficiency is compared to that obtained by means of the conventional method of moments (MM), modified maximum likelihood (MML) method and the usual maximum likelihood (ML) method. These intensive simulations reveal that MML estimators are the best in most of the cases, and the L-moment estimators are less subject to bias in estimation for some mixtures and more efficient in most of the cases than the conventional MM estimators. The L-moment estimators are, in some cases, more efficient than the ML and MML estimators.     

A Numerical Study of Small Parameter Behavior of Some Families of Distributions

Limiting distributions play an important role in approximating the exact distributions, especially when they have a rather cumbersome analytic form, or simply when they do not have a closed from. The question that naturally arises is how good the approximation is. In this article, we propose a procedure for the numerical assessment of the “goodness” of some easy-to-calculate limiting distributions, originally proposed in Bar-Lev and Enis, in various cases of the underlying distributions, some of which are inherently computationally challenging. The details of the procedure are provided in three examples. The first example deals with the gamma distributions; the second deals with Bessel distributions related to a symmetric random walk, and the third example deals with positive stable distributions. The details of two additional variations of these examples are also discussed. These examples illustrate the ease with which the limiting approximations could be applied in the various cases, well-demonstrating their computational simplicity and attractiveness.     

Distribution of the product of a pair of independent two-sided power variates

ABSTRACT

The distributions of algebraic functions of random variables are important in theory of probability and statistics and other areas such as engineering, reliability, and actuarial applications, and many results based on various distributions are available in the literature. The two-sided power distribution is defined on a bounded range, and it is a generalization of the uniform, triangular, and power-function probability distributions. This paper gives the exact distribution of the product of two independent two-sided power-distributed random variables in a computable representation. The percentiles of the product are then computed, and a real data application is given.     

短期波动对长期增长的效应 ——基于省际面板数据的经验证据

 短期波动对长期增长的效应如何具有重要的政策含义，本文旨在从一般的意义上对我国短期波动对长期增长的效应进行经验分析。使用1953-2004年我国27个省级地区经济波动和增长的面板数据及两种数据形式和计量方法，我们发现：20世纪90年代以前我国各地区短期波动对长期增长具有相同的负面效应，然而，20世纪90年代以后，各地区短期波动对长期增长的效应具有异质性，有的地区该效应为正，有的地区为负。     

企业年报数据中工业增加值异常情况的诊断

长期以来,我国政府对统计数据的质量极为重视,并通过各级统计人员的不懈努力,已经探索出一套较为完整的、准确的和有效的控制数据质量的措施和方法,积累了相当丰富的实际操作经验,对提高统计数据质量起到了必不可少的作用。但是,这些措施和方法更偏重于具体细则的实施和实际经验的运用,缺少控制数据质量方法的介入。特别是在不同经济模式下,统计数据摆动相当显著,仅凭经验判断虚假数据就远远不能满足要求。形势迫切地要求我们除了加大政策和法规实施力度外,还必须尽快引进现代统计方法,实现从经验到经验和方法论相结合的过渡,以…     

从统计学史解析“自由度”概念

自由度是统计学中一个十分重要而又长期没有被圆满解释的概念。对此,从统计学史角度,对皮尔逊、费歇尔有关自由度问题争论原始文献细致考察,彻底澄清了自由度概念的内涵及与其相关的统计思想,弥补了Fienberg、Stigler与陈希孺已有解释的缺陷。研究表明：皮尔逊关于卡方检验中无论总体分布已知还是其来自于样本推断统计量都具有同一分布的错误判断,导致卡方检验的准确性出现偏差,这种偏差虽被同时代少数几个统计学家察觉但他们却无法解释其根源。费歇尔提出自由度概念并结合n维几何、假设检验与最大似然方法的论证不仅修正了皮尔逊的错误,也完善了从样本统计量估计总体参数的数理逻辑。     

我国内外资工业企业能源消耗特点分析

基于2007年区分内外资企业的非竞争型能源投入占用产出表,本文测算了我国工业内、外资企业的直接综合能耗强度与完全综合能耗强度差异,并从宏观角度分析了用于满足消费、投资和出口需求时,工业各部门内、外资企业的完全综合用能情况。分析结果表明,我国工业内、外资企业的用能效率存在显著差异。就单位产值的完全综合能耗而言,外资企业比同部门的内资企业要低10%-40%左右。因此,在满足同等比重的最终需求时,外资企业比相应的内资企业耗能更低。特别是在出口的生产上,外资企业在满足了我国61%的商品出口需求的同时,其完全综合用能仅占出口用能的53%。该测算对我国相关工业技术节能的政策制定具有重要参考意义。     

Estimation of an indicator of the representativeness of survey response

Nonresponse is a major source of estimation error in sample surveys. The response rate is widely used to measure survey quality associated with nonresponse, but is inadequate as an indicator because of its limited relation with nonresponse bias. Schouten et al. (2009) proposed an alternative indicator, which they refer to as an indicator of representativeness or R-indicator. This indicator measures the variability of the probabilities of response for units in the population. This paper develops methods for the estimation of this R-indicator assuming that values of a set of auxiliary variables are observed for both respondents and nonrespondents. We propose bias adjustments to the point estimator proposed by Schouten et al. (2009) and demonstrate the effectiveness of this adjustment in a simulation study where it is shown that the method is valid, especially for smaller sample sizes. We also propose linearization variance estimators which avoid the need for computer-intensive replication methods and show good coverage in the simulation study even when models are not fully specified. The use of the proposed procedures is also illustrated in an application to two business surveys at Statistics Netherlands.     

农村义务教育经费保障机制改革的成效评价

“新机制”改革的核心任务是,建立农村义务教育财政投入的长效机制,其成效评价应该是重点考察它的财政投入效应。利用FRDD方法,对2006年“新机制”改革的实证研究表明,在数量上,西部农村地区的人均义务教育财政投入确实得到了显著提高;在财政资源配置结构上,西部农村落后地区获得了更多转移支付,而中等收入地区的义务教育财政投入水平仍然较低,财政中立性原则没有得到充分体现;在管理制度上,“新机制”改革没能有效提高县级政府的义务教育财政努力程度,存在显著的挤出效应,降低了财政资源的使用效率。     

Construction of Simultaneous Confidence Intervals for Ratios of Means of Lognormal Distributions

For constructing simultaneous confidence intervals for ratios of means for lognormal distributions, two approaches using a two-step method of variance estimates recovery are proposed. The first approach proposes fiducial generalized confidence intervals (FGCIs) in the first step followed by the method of variance estimates recovery (MOVER) in the second step (FGCIs–MOVER). The second approach uses MOVER in the first and second steps (MOVER–MOVER). Performance of proposed approaches is compared with simultaneous fiducial generalized confidence intervals (SFGCIs). Monte Carlo simulation is used to evaluate the performance of these approaches in terms of coverage probability, average interval width, and time consumption.     

Two separate effects of variance heterogeneity on the validity and power of significance tests of location

Heterogeneity of variances of treatment groups influences the validity and power of significance tests of location in two distinct ways. First, if sample sizes are unequal, the Type I error rate and power are depressed if a larger variance is associated with a larger sample size, and elevated if a larger variance is associated with a smaller sample size. This well-established effect, which occurs in t and F tests, and to a lesser degree in nonparametric rank tests, results from unequal contributions of pooled estimates of error variance in the computation of test statistics. It is observed in samples from normal distributions, as well as non-normal distributions of various shapes. Second, transformation of scores from skewed distributions with unequal variances to ranks produces differences in the means of the ranks assigned to the respective groups, even if the means of the initial groups are equal, and a subsequent inflation of Type I error rates and power. This effect occurs for all sample sizes, equal and unequal. For the t test, the discrepancy diminishes, and for the Wilcoxon–Mann–Whitney test, it becomes larger, as sample size increases. The Welch separate-variance t test overcomes the first effect but not the second. Because of interaction of these separate effects, the validity and power of both parametric and nonparametric tests performed on samples of any size from unknown distributions with possibly unequal variances can be distorted in unpredictable ways.     

我国R&D状况的区域比较分析

一、引言科学研究与试验发展 (Ｒ＆Ｄ)活动是指在科学技术领域 ,为增加知识总量、以及运用这些知识去创造新的应用而进行的系统的、创造性的活动 ,包括基础研究、应用研究、试验发展三类活动。科学研究与试验发展 (Ｒ＆Ｄ)活动在社会经济空间结构的演变中起着重要作用 ,已为我国及世界各国社会经济发展的史实所证明。然而 ,我国Ｒ＆Ｄ活动的总体水平不高 ,Ｒ＆Ｄ活动在研究领域、活动地域上发展不平衡 ,阻滞并影响了我国经济发展质量的提高和区域经济协调发展。鉴于此 ,本文通过将Ｒ＆Ｄ活动置于区域经济协调发展这一大系统中 ,对 2 0 0 0年…     

Isotonic estimation of survival under a misattribution of cause of death

Several authors have indicated that incorrectly classified cause of death for prostate cancer survivors may have played a role in the observed recent peak and decline of prostate cancer mortality. Motivated by the suggestion we studied a competing risks model where other cause of death may be misattributed as a death of interest. We first consider a na?ve approach using unconstrained nonparametric maximum likelihood estimation (NPMLE), and then present the constrained NPMLE where the survival function is forced to be monotonic. Surprising observations were made as we studied their small-sample and asymptotic properties in continuous and discrete situations. Contrary to the common belief that the non-monotonicity of a survival function NPMLE is a small-sample problem, the constrained NPMLE is asymptotically biased in the continuous setting. Other isotonic approaches, the supremum (SUP) method and the Pooled-Adjacent-Violators (PAV) algorithm, and the EM algorithm are also considered. We found that the EM algorithm is equivalent to the constrained NPMLE. Both SUP method and PAV algorithm deliver consistent and asymptotically unbiased estimator. All methods behave well asymptotically in the discrete time setting. Data from the Surveillance, Epidemiology and End Results (SEER) database are used to illustrate the proposed estimators.