A note on the determination of A-optimal type block designs under fixed and mixed effects models

In this paper, we consider the problem of estimating a selected set of contrasts between v treatments using a block design consisting of b blocks of size k. Traditionally, the construction of A-optimal block designs for such situations has been carried out assuming a fixed effects model. In this paper, we show that A-optimal designs constructed under a fixed effects model are robust in the sense that these designs have maximal minimal efficiency when considered among all available designs and under all possible mixed effects models. AMS 1991 subject classifications: Primary 62K05; Secondary 62K10     

SomeE andMV-optimal row-column designs having equal numbers of rows and columns

In this paper we consider experimental situations in whichv treatments are to be tested using a row-column design consisting ofb columns andb rows and wherev does not divideb ². Some sufficient conditions are obtained for a design to beE orMV-optimal in such an experimental setting and methods for constructing row-column designs satisfying the sufficient conditions obtained are also given. This research was supported by NSF Grant No. DMS-8401943.     

A note on theE-optimality of block designs

Summary In this paper we consider the problem of determiningE-optimal block designs for experimental situations in whichv treatments are to be tested onn experimental units arranged inb blocks and where the block sizes and number of replications assigned to the treatments are allowed to vary. Some sufficient conditions are obtained for designs to beE-optimal in these situations and methods for constructing designs which satisfy the sufficient conditions given are also derived.     

Robustness to the unavailability of data in block designs

We present general results for finding or boundingt _maxB , the maximum number of arbitrary whole blocks of observations which can be removed from a block design, and still leave all of the elementary treatment contrasts estimable. The block sizes may be larger than the number of treatments. The results are applied to BBDs, reinforced BIBDs and BBDs, BTIBDs, and a series of variance balanced incomplete block designs with two block sizes. Also given for most of these designs, are results fort _max, the maximum number of arbitrary, scattered observations that can become unavailable, and still leave all of the elementary treatment contrasts estimable.The work was undertaken while Dr. Whittinghill was visiting Ohio State University, and supported by a grant from the Natural Sciences Division, Colby College, Waterville, Maine.     

TypeS designs with nested rows and columns

Summary Supplemented balance in block designs with nested rows and columns is considered, under the name of typeS designs with nested rows and columns. Analysis and construction of such designs are also discussed.     

The existence of sampling designs with preassigned inclusion probabilities

Summary The question of the existence of a sampling design realizing given preassigned inclusion probabilities is treated. The question can be fully answered in the case of inclusion probabilities of first order. If the inclusion probabilities of second order are given it is shown why necessary and sufficient conditions for the existence of a corresponding sampling design can be derived only in very special cases.     

A note on generalized aberration in factorial designs

In this paper we extend the wordlength pattern and minimum aberration for non-regular factorials. The new concepts, the generalized wordlength pattern and minimum generalized aberration, are proposed. Some connections between the generalized wordlength pattern and uniformity are given. Some applications of the new concepts in the Blackett and Burman's designs are discussed. Received: September 2000     

Optimality and efficiency of small chessboard designs for correlated errors

Optimal p × q row–column designs are obtained via complete enumeration of all possible designs for two treatments in some fixed effects models with errors specified by a doubly geometric covariance structure. This is done, in part, by a computer search, for a finite set of sizes of the correlation coefficients and in cases where p and q are small enough to make such a search feasible.     

A series of resolvable PBIB(3) designs with two replicates

A new series of resolvable PBIB(3) designs with two replications has been proposed along with a simple method of analysis. These designs form a generalization of circular lattice designs of Rao (1956).     

A note on a specification test of independence

In a recent paper Zheng (1997a) proposed a new specification test of independence between two random vectors by the kernel method. He showed asymptotic normality under the hypothesis and local alternatives. The present work investigates the asymptotic distribution of the corresponding test statistic under fixed alternatives. In this case asymptotic normality of a standardized statistic is still valid but with a different rate of convergence. Received: January 1999     

A note on the robustness of Box-Behnken designs to the unavailability of data

Box-Behnken designs and central composite designs are efficient designs for fitting second order polynomials to response surfaces, because they use relatively small numbers of observations to estimate the parameters. In this paper we investigate the robustness of Box-Behnken designs to the unavailability of observations, in the sense of finding t _max , the maximum number of arbitrary rows in the design matrix that can be removed and still leave all of the parameters of interest estimable. The results are compared to the known results for the central composite designs found in MacEachern, Notz, Whittinghill & Zhu (1995). The blocked Box-Behnken designs are equally as robust as those that are not blocked. Received December 1997     

Conditional assessment of the impact of a Hausman pretest on confidence intervals

In the analysis of clustered and longitudinal data, which includes a covariate that varies both between and within clusters, a Hausman pretest is commonly used to decide whether subsequent inference is made using the linear random intercept model or the fixed effects model. We assess the effect of this pretest on the coverage probability and expected length of a confidence interval for the slope, conditional on the observed values of the covariate. This assessment has the advantages that it (i) relates to the values of this covariate at hand, (ii) is valid irrespective of how this covariate is generated, (iii) uses exact finite sample results, and (iv) results in an assessment that is determined by the values of this covariate and only two unknown parameters. For two real data sets, our conditional analysis shows that the confidence interval constructed after a Hausman pretest should not be used.     

A note on distortions from estimating the regional impacts of exogenous changes in output

This paper demonstrates both theoretically and empirically that when outputs instead of final demands are exogenously predetermined, the traditional Leontief final demand model overestimates economic impact, and even more so in a multiregional context. We assess this premise vis-à-vis the Leontief output model using the 2013 interregional input–output table of the Republic of Korea. We find that from a multiregional perspective the standard Leontief final demand model yields substantially biased output multipliers for Chungbuk Province.     

A new method for automatic synthesis of tolerances for complex assemblies based on polychromatic sets

In computer-aided tolerance design (CAT), integrated design of dimensional and geometric tolerances is still one of the research hotspots. Polychromatic sets theory (PST) is a new mathematic tool, which is especially suitable for formal hierarchical structure models. Based on PST, in this article, a new hierarchical representation model for tolerance synthesis is presented to realise integrated design of dimensional and geometric tolerances. According to the inference relations between unified and individual colours of PST, the synthesis matrices of variational geometric constraints (VGC) are established in the VGC tier of the model, and the synthesis matrices of tolerance types are established in the tolerance type tier of the model. On this basis, the synthesis processes from the feature tier to the VGC tier and from the VGC tier to the tolerance type tier can be realised. VGCs, which are achieved by the synthesis matrices of VGCs, can be combined together to establish a well-constrained VGC network (VGCN). Tolerance types, which are achieved by the synthesis matrices of tolerance types, can be added to the well-constrained VGCN to construct a well-constrained tolerance network. An application example is given in the article to illustrate the synthesis steps.     

A note on the projection properties of Hadamard matrices obtained by the first Payley construction

We show that the projections on four factors of an arbitrary orthogonal array of strength 2 allow the estimation of main effects and two-factor interactions when all other effects are assumed to be zero, if those projections satisfy the bounds given by Weils theorem. The only exceptions are the Hadamard matrices of orders 16 and 24. A consequence is again the estimability of main effects and two-factor interactions for the projections on four factors of the first Payley construction for arbitrary run size.     

基于局部网络效应的创新扩散分析

在考虑局部网络效应的基础上,采用微观扩散模型仿真分析创新扩散。研究表明,局部网络效应使得创新潜在采纳个体决策相互影响,从而导致这种采纳者之间微观交互模式所呈现的宏观社会网络结构影响创新扩散的速度和程度。即使某些创新收益非常高,也有可能因为创新潜在采纳个体之间交互模式的影响而导致其扩散最终失败。同时早期创新采纳个体一般具有社会联系比较广泛,自身采纳阈值较高,自身局部网络效应强度较小,更关注创新内在价值等创新特征。     

基于实物期权法的风险投资项目估价方法——一个文献综述

本文理清了实物期权及其在风险投资项目估价中应用的发展脉络,并提出了实物期权在风险投资项目估价应用中需要发展的地方。     

国家审计推进经济高质量发展的作用研究——基于地级城市面板数据的空间计量分析

采用空间杜宾模型和2006—2016年我国283个地级及以上城市的面板数据,探讨了国家审计对城市经济发展质量的影响及其空间效应。结果表明,国家审计能显著提升本地区经济发展质量,但对周边地区产生了负向空间外溢效应;国家审计对本地和周边地区经济发展质量的影响是对动能转换、结构升级、发展效率、节能减排、成果分享五个方面作用机制影响的综合反映,且对结构升级、节能减排、成果分享的作用效果尤为明显。进一步研究发现,Ⅱ型大城市和中等城市的国家审计有助于促使本地区经济发展质量提升,但对周边城市却有明显的抑制作用;而Ⅰ型及以上大城市和小城市的国家审计对本地和周边城市经济发展质量均未产生明显影响。结果表明,强化国家审计功能、推进跨区域协同审计,对于推进经济高质量发展具有重要意义。