2(n1+n2)-(k1+k2) Fractional factorial split-plot designs containing clear effects

Whole-plot (WP) factors and sub-plot (SP) factors play different roles in fractional factorial split-plot (FFSP) designs. In this paper, we consider FFSP designs with resolution III or IV from the viewpoint of clear factorial effects, classify two-factor interactions (2FIs) into three types, and give sufficient and necessary conditions for the existence of FFSP designs containing various clear factorial effects, including two types of main effects and three types of 2FIs. The structures of these designs are also shown and illustrated with examples.     

Construction and selection of tightened-normal-tightened sampling inspection scheme of type TNT-(n1, n2; c)

A table is presented for the construction and selection of tightened-normal-tightened sampling scheme of type TNT-(n1, n2;c). Efficiency of TNT-(n1, n2;c) scheme over conventional single and double sampling plans is discussed.     

Sufficient m-out-of-n (m/n) bootstrap

Traditional resampling methods for estimating sampling distributions sometimes fail, and alternative approaches are then needed. For example, if the classical central limit theorem does not hold and the naïve bootstrap fails, the m/n bootstrap, based on smaller-sized resamples, may be used as an alternative. An alternative to the naïve bootstrap, the sufficient bootstrap, which uses only the distinct observations in a bootstrap sample, is another recently proposed bootstrap approach that has been suggested to reduce the computational burden associated with bootstrapping. It works as long as naïve bootstrap does. However, if the naïve bootstrap fails, so will the sufficient bootstrap. In this paper, we propose combining the sufficient bootstrap with the m/n bootstrap in order to both regain consistent estimation of sampling distributions and to reduce the computational burden of the bootstrap. We obtain necessary and sufficient conditions for asymptotic normality of the proposed method, and propose new values for the resample size m. We compare the proposed method with the naïve bootstrap, the sufficient bootstrap, and the m/n bootstrap by simulation.     

One-sample distribution-free test statistic V(n,k) sensitive to location differences

A location sensitive one—sample test V(n,n) similar to the Wilcoxon two—sample test was proposed by Riedwyl (1967) and stuided by Carnal and Riedwyl (1972). A generalization for grouped data was given by Maag, Streit and Drouilly (1973). In the present paper we discuss the application of the test for grouped data. We present a table of the significance limits and discuss the approximation by means of the normal distribution.     

Revealing the dependence structure between X(1) and X(n)

In this paper we address the dependence structure of the minimum and maximum of n iid random variables X₁,…,X_n by determining their copula. It is then easy to give an alternative proof for their asymptotic independence and to calculate Kendall's τ and Spearman's ρ for (X₍₁₎,X_(n)). This will show that the dependence between the variables is already small for small sample sizes. Finally, it can be shown that 3τ_n⩾ρ_n⩾τ_n>0. Although closed-form expressions are available for τ_n and ρ_n, we cannot compare them directly but have to use the concept of positive likelihood ratio dependence to establish this result.     

An approximate fractional Gaussian noise model with $$mathcal {O}(n)$$ O ( n ) computational cost

Statistics and Computing - Fractional Gaussian noise (fGn) is a stationary time series model with long-memory properties applied in various fields like econometrics, hydrology and climatology. The...     

Procedures and tables for the selection of tightened-normal-tightened (TNT-( n ; c 1 , c 2 )) sampling schemes

Procedures for the selection of tightened-normal-tightened (TNT) sampling schemes of type TNT-( n ; c 1 , c 2 ) are presented. It is shown that the TNT scheme provides a smaller sample size than the matched single-sampling plan.     

Multivariate normal estimation: the case (n < p)

Estimation in the multivariate context when the number of observations available is less than the number of variables is a classical theoretical problem. In order to ensure estimability, one has to assume certain constraints on the parameters. A method for maximum likelihood estimation under constraints is proposed to solve this problem. Even in the extreme case where only a single multivariate observation is available, this may provide a feasible solution. It simultaneously provides a simple, straightforward methodology to allow for specific structures within and between covariance matrices of several populations. This methodology yields exact maximum likelihood estimates.     

Optimized algorithms for computing Wilcoxon's T n,Wilcoxon's W m,n and Ansari-Bradley's A m,n statistics when m and n are small

Wilcoxon's signed rank sum test, Wilcoxon's rank sum test and the Ansari-Bradley rank test are three well-known distribution-free tests. When the sample size is large enough, the lower tail probabilities P 0 {T n /< = x} , P 0 {W m,n /< = x} and P 0 {A m,n /< = x} may be easily computed, under H 0 , using some normal approximations. When the size of the samples is too small, these normal approximations become insufficient. Therefore, the main goal of our work is to find some fast algorithms which compute the exact lower tail probabilities P 0 {T n /< = x}, P 0 {W m,n /< = x} and P 0 {A m,n /< = x} when the normal approximation is inefficient.     

Index to Articles,by Author,Volume 2 (1984)

This article investigates the statistical properties of the U.S. sacrifice ratio—the cumulative output loss arising from a permanent reduction in inflation. We derive estimates of the sacrifice ratio from three structural vector autoregression models and then conduct a series of simulation exercises to analyze their sampling distribution. We obtain point estimates of the sacrifice ratio that are consistent with results reported in earlier studies. However, the estimates are very imprecise, which we suggest reflects the poor quality of instruments used in estimation. We conclude that the estimates provide a very unreliable guide for assessing the output cost of disinflation policy.     

Designing ChSP-4(c1, c2) plans

In this paper, the notion of average total inspection (ATI) is introduced to ChSP-4(c1,c2) sampling plans. Procedures have been developed for the construction and selection of ChSP-4(c1, c2 plans, minimizing ATI at a given process average, while protection to the consumer is given in terms of the (i) average outgoing quality limit and (ii) limiting quality level.A wide range of c1 and c2 values are considered for developing tables which cover almost all practical situations. The procedure described is similar to that of Dodge and Romig.     

数字解码(二)

生命进化知识解码（上）生命探索 自古以来,人类对生命之探索一直很有兴趣。大家都知道母鸡生蛋,蛋孵小鸡,树木结出果子,生产种子,种子种植成树木。然而,最初的鸡或鸡蛋从何而来？最初的树木或种子从何而来？在探索生命过程中, １４０年前达尔文提出的“进化论”思想无疑的带来极大的震撼,引发人们对过去与未来的省思。但可能很多人不知道,统计数字与进化论之发展,两者间早就有密切之关联。在古希腊时代,巴曼尼狄思认为宇宙是一套永恒不变的绝对系统,现象领域中所见到的变化,不过是一些不能变的微粒,经过重新“排列组合”所产…     

Two-stage chain sampling plans chsp-(0,2) and chsp-(l,2) - part 1

This article outlines the structure of a generalized family of two-stage chain sampling plans, extending the concept of two-stage chain sampling plans of Dodge and Stephens (1966) which is an extension of the original work of Dodge (1955). Expressions are derived for the OC curves for two-stage chain sampling plans with (c₁,c₂) = (0,2) and (1,2). In the original work of Dodge (1955) only acceptance numbers of 0,1 were used and in the extension work of Dodge and Stephens (1966) acceptance numbers of (c₁,c₂) = (0,1), (0,2), (1,2), (0,3), (1,3), (0,4) and (1,4) were used with selected sets of values of k₁ and k₂ (the number of lots considered for cumulation in the first and second stage respectively). In this paper the OC curves are derived more generally for any k₁ and k₂combination for two-stage chain sampling plans with (c₁,c₂) = (0,2) and (1,2) and comparisons are made with respect to sample sizes and discriminating power, with the corresponding single and double sampling plans.     

Classification of affine resolvable 2-(27, 9, 4) designs

All affine resolvable designs with parameters of the design of the hyperplanes in ternary affine 3-space are enumerated. This enumeration implies the classification (up to equivalence), of all optimal equidistant ternary codes of length 13 and distance 9, as well as all complete orthogonal arrays of strength 2 with 3 symbols, 13 constraints and index 3. Up to isomorphism, there are exactly 68 such designs. The automorphism groups and the rank of the incidence matrices over GF(3) are computed. There are six designs with point-transitive automorphism groups, and one design with trivial group. The affine geometry design is the unique design with lowest 3-rank, and the only design with 2-transitive automorphism group.     

GDDS范例--孟加拉国(下)

表B.数据类别和指标 按每一个指标填报。孟加拉国统计局要填报国民账户总量、生产指数、价格指数和劳动力市场指标等4张数据类别表。现以国民账户总量表中的核心指标国内生产总值(名义和实际)来说明表B的内容。一、数据特征 范围：简单说明数据的主要特征，即用户为了适当使用数据所必须了解的特点。包括计算单位、范围(如地理、机构和产品范围)、统计特征(如季度调整、指数基年)、基本数据源和会计方法。 孟加拉国统计局每年(头年7月－来年6月的财年)编制和公布下列数据：按产业活动和支出分类以现行市场价格计算的国内生产总值…