Nonparametric multiple comparison procedures for unbalanced two-way layouts

In this paper, we consider nonparametric multiple comparison procedures for unbalanced two-way factorial designs under a pure nonparametric framework. For multiple comparisons of treatments versus a control concerning the main effects or the simple factor effects, the limiting distribution of the associated rank statistics is proven to satisfy the multivariate totally positive of order two condition. Hence, asymptotically the proposed Hochberg procedure strongly controls the familywise type I error rate for the simultaneous testing of the individual hypotheses. In addition, we propose to employ Shaffer's modified version of Holm's stepdown procedure to perform simultaneous tests on all pairwise comparisons regarding the main or simple factor effects and to perform simultaneous tests on all interaction effects. The logical constraints in the corresponding hypothesis families are utilized to sharpen the rejective thresholds and improve the power of the tests.     

Estimation in a linear regression model under the Kullback–Leibler loss and its application to model selection

This paper is concerned with the problem of constructing a good predictive distribution relative to the Kullback–Leibler information in a linear regression model. The problem is equivalent to the simultaneous estimation of regression coefficients and error variance in terms of a complicated risk, which yields a new challenging issue in a decision-theoretic framework. An estimator of the variance is incorporated here into a loss for estimating the regression coefficients. Several estimators of the variance and of the regression coefficients are proposed and shown to improve on usual benchmark estimators both analytically and numerically. Finally, the prediction problem of a distribution is noted to be related to an information criterion for model selection like the Akaike information criterion (AIC). Thus, several AIC variants are obtained based on proposed and improved estimators and are compared numerically with AIC as model selection procedures.     

The use of edge-directions and linear programming to enumerate vertices

Given a list of vectors that contains directions of the edges of a given polytope ℘ and the availability of an algorithm that solves linear programs over ℘, we describe a method for enumerating the vertices of ℘; in particular, the method is adaptable to polytopes which are presented as (linear) projections of polytopes having linear inequality representation. Polynomial complexity bounds under both the real and the binary computation models are derived when the dimension of the polytope is fixed and the given LP algorithm is polynomial. Dedicated to Professor Frank K. Hwang on the occasion of his sixty fifth birthday. Supported in part by a grant from ISF—the Israel Science Foundation, by a VPR grant at the Technion and by the Fund for the Promotion of Research at the Technion.     

Two-dimensional balanced sampling plans excluding adjacent units

Hedayat et al. [Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159–170, Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.), Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575–583] first introduced balanced sampling plans for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. While significant advancements have been made in the identification and generalizations of such plans—commonly referred to as BSA sampling plans—little is known concerning the extension of such sampling plans to multi-dimensional populations. This paper will present a review of the pertinent results of one-dimensional BSA sampling plans and a discussion concerning the properties of two-dimensional BSA sampling plans.     

光度分析中工作曲线的线性回归及计算

提出了应用线性回归求算光度分析工作曲线方程的方法及应用电脑处理滴定数据的ＢＡＳＩＣ程序。     

Exact simultaneous confidence segments for all contrast comparisons

This paper provides an exact method to construct simultaneous confidence bands for all contrasts of several regression lines over a restricted explanatory variable. Due to the lack of exact methods in the literature, currently existing approaches consist mainly of simulation based approaches. Using confidence bands for regression analysis occurs ubiquitously in practice, for example, inference on the shelf-life or stability of a drug, on the reliability of an engineering system over time, on the environmental impact of a fertilizer in a field over time, to list just a few. The new method enhances currently existing approaches that are based on simulations.     

On generalized order statistics from linear exponential distribution and its characterization

In this paper, recurrence relations for single and product moments of generalized order statistics (gOSs) from linear exponential distribution (LE) are derived and characterizations of this distribution based on the conditional moments of the gOSs are given.     

Estimation of a linear model in transformed variables under microaggregation by individual ranking

We consider the least squares estimation of a linear regression model in transformed variables from a data set that has been microaggregated by means of the individual ranking method. It is shown that the least squares estimators are consistent even in the case where variable transformations are carried out after microaggregation. Applying individual ranking techniques to a data set thus guarantees the analytical validity of the microaggregated data for a wide class of statistical models.     

Estimation of linear models with anonymised panel data

The paper analyses the biasing effect of anonymising micro data by multiplicative stochastic noise on the within estimation of a linear panel model. In short panels, additional bias results from serially correlated regressors. Results in this paper are related to the project “Firms’ Panel Data and Factual Anonymisation,” which is financed by Federal Ministry of Education and Research. We would like to thank the anonymous referees for helpful comments.