Distributional Studies and the Computer: An Analysis of Durbin's Rank Test

A study of the distribution of a statistic involves two major steps: (a) working out its asymptotic, large n, distribution, and (b) making the connection between the asymptotic results and the distribution of the statistic for the sample sizes used in practice. This crucial second step is not included in many studies. In this article, the second step is applied to Durbin's (1951) well-known rank test of treatment effects in balanced incomplete block designs (BIB's). We found that asymptotic, χ², distributions do not provide adequate approximations in most BIB's. Consequently, we feel that several of Durbin's recommendations should be altered.     

The connectedness and optimality of a class of row-column designs

Balanced Incomplete Block Designs have been employed as row-column designs by a number of researchers. In this paper necessary and sufficient conditions for the connectedness of such designs are obtained, and methods for their optimisation are presented. The optimal design is shown to be always connected.     

Application of minque procedure to block designs

Method of minimum norm quadratic unbiased estimation (MINQUE) is applied to incomplete block designs. Simple formulae are derived for a class of designs which includes the balanced designs.     

Efficient Block Designs for Dependent Observations—A Computer-Aided Search

In this article, the exchange and interchange algorithm of Zergaw (1989 Zergaw , G. ( 1989 ). A sequential method of constructing optimal block designs . Austral. J. Statist. 31 : 333 – 342 .[Crossref] , [Google Scholar]) and Martin and Eccleston (1992 Martin , R. J. , Eccleston , J. A. ( 1992 ). Recursive formulae for constructing block designs with dependent errors . Biometrika 79 : 426 – 430 .[Crossref], [Web of Science ®] , [Google Scholar]) have been modified and used for searching efficient block designs for making all possible pairwise treatment comparisons when observations are dependent. The lower bounds to the A- and D-efficiencies of the designs in a given class of the designs have been obtained for correlated observation structure and the procedure of computing lower bounds to A- and D-efficiencies has been incorporated in the algorithm. The algorithm has been translated into a computer program using Microsoft Visual C++. Using this program, a search for efficient designs for making all possible pairwise treatment comparisons has been made for v ≤ 10, b ≤ 33, k ≤ 10 such that bk ≤ 100 and v > k. The block designs considered are usual block designs (rectangular block designs) and circular block designs. Nearest neighbor (NN), autoregressive of order 1 (AR(1)) correlation structures are studied. The ranges of correlation coefficients for different correlation structures investigated are |ρ|≤0.50 for NN correlation structure in rectangular blocks, |ρ|≤0.45 for NN correlation structure in circular blocks, and |ρ|≤0.95 for AR(1) correlation structure. For these ranges, the matrix of correlation coefficients among observations within a block is positive definite. Robustness aspects of designs that are efficient for a given value of correlation have been investigated against other values of correlation coefficients. Robustness aspects of designs that are efficient for independent observations have also been studied for experimental situations with dependent observations.     

Resampling Methods for Time Series Level Crossings

We present an application of subsampling and bootstrap methods for time series to determine the distribution of the estimator of zero crossings. The zero crossings method provides an alternative estimator of the lag-1 autocorrelation coefficient that is reducing the data storage requirements and is more robust with respect to outliers when compared to the classical estimator. The main results here are showing the consistency of subsampling, the consistency of moving block bootstrap, the consistency of non overlapping block bootstrap and the consistency of stationary bootstrap for this estimator. Theorems are formulated for Gaussian processes, elliptically symmetric processes and processes which are transformed Gaussian processes. Theoretical results are illustrated by simulations and practical data analysis. We have also shown that in practice the MBB method behaves better than the subsampling method.     

用文化品牌刷新历史街区

以广州十三行历史街区为例,主张保护复兴历史名城,应遵循其固有文化的本质特征、繁衍脉络,立足于文化的物质载体、空间环境进行有机化康复更新,以此创建文化品牌,保养自身活力,打造高格调、高档次的国际化文化旅游产业,实现可持续发展。     

On additive and block decompositions of WLSEs under a multiple partitioned regression model

While considering the mechanism of weighted least-squares estimators (WLSEs) of regression coefficients in a partitioned linear model, Tian and Takane [On sum decompositions of weighted least-squares estimators under the partitioned linear model, Comm. Statist. Theory Methods 37 (2008), pp. 55–69] gave some identifying conditions for the WLSEs to be the sum of WLSEs under its two small models based on orthogonality of regressors with respect to the given weight matrix. The purpose of this paper is to show how to establish additive and block decompositions of WLSEs under a multiple partitioned linear model and its k small models based on orthogonality of regressors with respect to a given weight matrix.     

Estimation of a response surface from-a general incomplete block design

If an incomplete block design is used to compare v treatments and later it is decided to fit a second order response surface using the fact that the v treatments are v combinations of levels of m different factors, how will one proceed to obtain this? This paper demonstrates how the usual analysis of an incomplete block design with or without recovery of interblock information can be augmented to yield estimates of response surface coefficients.     

Balanced block designs

In the present paper an attempt has been made to characterize and unify the three different concepts of balancing in incomplete block designs, namely (i) variance balance, (ii) efficiency balance and (iii) pairwise balance. Simple characterizations of variance balance and efficiency balance have been given using the P matrix. A method of constructing efficiency balanced (EB) and variance balanced designs has also been presented.     

The robustness of chain block designs and coat-of-mail designs

Chain block designs are relatively vulnerable to loss of information when missing values or outliers may occur. An alternative class of designs, coat-of-mail designs, are proposed and the relative robustness of the two types of design are compared.