Two-level Orthogonal and Saturated Designs for Estimating Main Effects and Certain Important Interactions

In a two-level factorial experiment, we consider orthogonal designs that allow joint estimation of the grand mean, all main effects, and certain classes of two-level interactions, assuming that the remaining effects are all negligible. Based on a judicious allocation of the factorial effects of interest to the columns of a Hadamard matrix, we propose some general classes of orthogonal and saturated designs which include some existing orthogonal main-effect plans of asymmetric factorials as special cases.     

Construction of nested space-filling designs using difference matrices

Experiments that study complex real world systems in business, engineering and sciences can be conducted at different levels of accuracy or sophistication. Nested space-filling designs are suitable for such multi-fidelity experiments. In this paper, we propose a systematic method to construct nested space-filling designs for experiments with two levels of accuracy. The method that makes use of nested difference matrices can be easily performed, many nested space-filling designs for experiments with two levels of accuracy can thus be constructed, and the resulting designs achieve stratification in low dimensions. In addition, the proposed method can also be used to obtain sliced space-filling designs for conducting computer experiments with both qualitative and quantitative factors.     

Clustering algorithm for proximity-relation matrix and its applications

In this paper, we present a new algorithm for clustering proximity-relation matrix that does not require the transitivity property. The proposed algorithm is first inspired by the idea of Yang and Wu [16] then turned into a self-organizing process that is built upon the intuition behind clustering. At the end of the process subjects belonging to be the same cluster should converge to the same point, which represents the cluster center. However, the performance of Yang and Wu's algorithm depends on parameter selection. In this paper, we use the partition entropy (PE) index to choose it. Numerical result illustrates that the proposed method does not only solve the parameter selection problem but also obtains an optimal clustering result. Finally, we apply the proposed algorithm to three applications. One is to evaluate the performance of higher education in Taiwan, another is machine–parts grouping in cellular manufacturing systems, and the other is to cluster probability density functions.     

Exact moments of lawless and wang's operational ridge regression estimator

Assuming the disturbances are normally distributed, we derive expressions for, and simple conditions for the existence of the exact bias and matrix of second order moments of the Lawless and Wang Operational Ridge Regression estimator.     

景观生态学在合肥市绿地系统规划中的应用分析

利用景观生态学的斑块-廊道-基质理论、景观异质性理论及生物多样性理论对合肥市绿地系统规划进行应用分析,指出合肥市绿地系统的优点与不足,并就此提出了改进措施,以期为进一步从生态学角度指导合肥市绿地系统规划提供参考。     

Simultaneous confidence bands and regions for log-location-scale distributions with censored data

In many areas of application, especially life testing and reliability, it is often of interest to estimate an unknown cumulative distribution (cdf). A simultaneous confidence band (SCB) of the cdf can be used to assess the statistical uncertainty of the estimated cdf over the entire range of the distribution. Cheng and Iles [1983. Confidence bands for cumulative distribution functions of continuous random variables. Technometrics 25 (1), 77–86] presented an approach to construct an SCB for the cdf of a continuous random variable. For the log-location-scale family of distributions, they gave explicit forms for the upper and lower boundaries of the SCB based on expected information. In this article, we extend the work of Cheng and Iles [1983. Confidence bands for cumulative distribution functions of continuous random variables. Technometrics 25 (1), 77–86] in several directions. We study the SCBs based on local information, expected information, and estimated expected information for both the “cdf method” and the “quantile method.” We also study the effects of exceptional cases where a simple SCB does not exist. We describe calibration of the bands to provide exact coverage for complete data and type II censoring and better approximate coverage for other kinds of censoring. We also discuss how to extend these procedures to regression analysis.     

Inference on P(Y < X) in Bivariate Rayleigh Distribution

This paper deals with the estimation of reliability R = P(Y < X) when X is a random strength of a component subjected to a random stress Y, and (X, Y) follows a bivariate Rayleigh distribution. The maximum likelihood estimator of R and its asymptotic distribution are obtained. An asymptotic confidence interval of R is constructed using the asymptotic distribution. Also, two confidence intervals are proposed based on Bootstrap method and a computational approach. Testing of the reliability based on asymptotic distribution of R is discussed. Simulation study to investigate performance of the confidence intervals and tests has been carried out. Also, a numerical example is given to illustrate the proposed approaches.     

A hierarchical eigenmodel for pooled covariance estimation

Summary.  Although the covariance matrices corresponding to different populations are unlikely to be exactly equal they can still exhibit a high degree of similarity. For example, some pairs of variables may be positively correlated across most groups, whereas the correlation between other pairs may be consistently negative. In such cases much of the similarity across covariance matrices can be described by similarities in their principal axes, which are the axes that are defined by the eigenvectors of the covariance matrices. Estimating the degree of across-population eigenvector heterogeneity can be helpful for a variety of estimation tasks. For example, eigenvector matrices can be pooled to form a central set of principal axes and, to the extent that the axes are similar, covariance estimates for populations having small sample sizes can be stabilized by shrinking their principal axes towards the across-population centre. To this end, the paper develops a hierarchical model and estimation procedure for pooling principal axes across several populations. The model for the across-group heterogeneity is based on a matrix-valued antipodally symmetric Bingham distribution that can flexibly describe notions of 'centre' and 'spread' for a population of orthogonal matrices.     

生长曲线模型中协方差矩阵的齐次和非齐次估计的可容许性

讨论了生长曲线模型(1.1)中协差矩阵的二次型估计在齐次和非齐次估计类中的可容许性问题,并得到了相应的充要条件。     

Symmetric pattern models: a latent variable approach to item non-response in attitude scales

This paper proposes a new approach to the treatment of item non-response in attitude scales. It combines the ideas of latent variable identification with the issues of non-response adjustment in sample surveys. The latent variable approach allows missing values to be included in the analysis and, equally importantly, allows information about attitude to be inferred from non-response. We present a symmetric pattern methodology for handling item non-response in attitude scales. The methodology is symmetric in that all the variables are given equivalent status in the analysis (none is designated a 'dependent' variable) and is pattern based in that the pattern of responses and non-responses across individuals is a key element in the analysis. Our approach to the problem is through a latent variable model with two latent dimensions: one to summarize response propensity and the other to summarize attitude, ability or belief. The methodology presented here can handle binary, metric and mixed (binary and metric) manifest items with missing values. Examples using both artificial data sets and two real data sets are used to illustrate the mechanism and the advantages of the methodology proposed.