On the relationship between the sample size and the number of variables in a linear regression model

The problem of determining the number of variables to be included in the linear regression model is considered under the assumption that the dependent and independent variables have a joint normal distribution. It is shown that for a given sample size n there exists an optimal number k₀ (0 ≤ k₀ < n-2) of variables among all independent variables in the model, such that the expectation of the mean squared error corresponding to the prediction equation with k₀ variables is minimal.Application of this result to ustepwise procedures is discussed.     

Identities and recurrence relations for order statistics corresponding to ncnidentically distributed variable

In this paper, we derive two simple identities and some recurrencerelations involving order statistics from a sample of size n in case there is a possibility of one or more outliers being present.     

Multivariate analysis for the two-period repeated measures crossover design with application to clinical trials

Multivariate analysis techniques are applied to the two-period repeated measures crossover design. The approach considered in this paper has the advantage over the univariate analysis approach proposed recently by Wallenstein and Fisher (1977) that the former does not require any specific structure on the variance-covariance matrix of the repeated measures factor. (It should be noted that sums and differences of observations over periods are used for all tests. Therefore, there are two matrices under consideration, one for sums and one for differences.) Tests of significance are derived using the Wilks? criterion, and the procedure is illustrated with a numerical example from the area of clinical trials.     

Balanced Treatment incomplete block (BTIB) designs for comparing treatments with a control: minimal complete sets of generator designs for k = 3, p = 3(1)10

Bechhofer and Tamhane (1981) proposed a new class of incomplete block designs called BTIB designs for comparing p ≥ 2 test treatments with a control treatment in blocks of equal size k < p + 1. All BTIB designs for given (p,k) can be constructed by forming unions of replications of a set of elementary BTIB designs called generator designs for that (p,k). In general, there are many generator designs for given (p,k) but only a small subset (called the minimal complete set) of these suffices to obtain all admissible BTIB designs (except possibly any equivalent ones). Determination of the minimal complete set of generator designs for given (p,k) was stated as an open problem in Bechhofer and Tamhane (1981). In this paper we solve this problem for k = 3. More specifically, we give the minimal complete sets of generator designs for k = 3, p = 3(1)10; the relevant proofs are given only for the cases p = 3(1)6. Some additional combinatorial results concerning BTIB designs are also given.     

Design issues for population growth models

We briefly review and discuss design issues for population growth and decline models. We then use a flexible growth and decline model as an illustrative example and apply optimal design theory to find optimal sampling times for estimating model parameters, specific parameters and interesting functions of the model parameters for the model with two real applications. Robustness properties of the optimal designs are investigated when nominal values or the model is mis-specified, and also under a different optimality criterion. To facilitate use of optimal design ideas in practice, we also introduce a website for generating a variety of optimal designs for popular models from different disciplines.     

Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data

We analyse data on abortion rate (AR) in Italy with a particular focus on different behaviours in different regions in Italy. The aim is to try to reveal the relationship between the AR and several covariates that describe in some way the modernity of the region and the condition of the women there. The data are mostly underdispersed and the degree of underdispersion also varies with the covariates. To analyse these data, recent techniques for flexible modelling of a mean and dispersion function in a double exponential family framework are further developed now in a generalized additive model context for dealing with the multivariate set-up. The appealing unified framework and approach even allow to semi-parametric modelling of the covariates without any additional efforts. The methodology is illustrated on ozone-level data and leads to interesting findings in the Italian abortion data.     

Modified repeated median filters

We discuss moving window techniques for fast extraction of a signal composed of monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust scale estimate such as the median absolute deviation about the median (MAD) to select an adaptive amount of trimming. Application of robust regression, particularly of the repeated median, has been suggested for improving upon the median in trend periods. We combine these ideas and construct modified filters based on the repeated median offering better shift preservation. All these filters are compared w.r.t. fundamental analytical properties and in basic data situations. An algorithm for the update of the MAD running in time O(log n) for window width n is presented as well.     

俄国现代化的空间特点

现代化进程不仅具有时间的考量,同时还具有空间的考量。世界各国的现代化无不在一定的空间条件下得以展开。气候、土壤、地形、植被等自然地理条件,对人类生活和社会发展具有重要影响。与西欧相比,俄国的自然气候条件对其经济发展、交通运输和国家体制的影响更大。俄国疆域辽阔,人口迁移频繁,民族和社会结构复杂,其现代化进程在不同地区差异明显。如果不对与空间组织机构和地理环境因素有关的问题综合体进行研究,就不可能充分地解释现代化的全过程,不可能揭示它所固有的普遍性和特殊性。     

复制·重整·回忆:欧阳修《集古录》的文化考察

欧阳修在其<六一居士传>中说道:"吾家藏书一万卷,集录三代以来金石遗文一千卷,有琴一张,有棋一局,而常置酒一壶",加上自己一老翁,是为"六一"."六一"条件之完成,与<集古录>关系密切,并且由于<集古录>,开创了新的学术领域,造就了欧阳修的金石学家地位.关于<集古录>的研究,主要有两个大方向,一是讨论成书经过和时代;一是针对其内容,肯定其在史学、文献学、考古学、校雠学、书法艺术、文学批评、理学思想(辟佛排老)等层面的意义与价值.该文尝试将视野转向物质文化的角度,从文人收藏文物的意识形态,探析<集古录>的文化特质.笔者概括了"复制"、"重整"与"回忆"三个层次,认为通过复制金石文字,重整文字所建立的历史体系,欧阳修确立了历史文化凭借物质以传承的观念.而<集古录跋尾>里的伤逝片段,又与拥有金石榻本、证成文明轨迹的无上愉悦,形成哀乐互显的对照.     

Effect of relational bullying on attitudes,behavior and injury among adolescent bullies,victims and bully-victims

This study examined whether dysfunctional correlates of relational bullying parallel those that have been found for physical bullying. We used data from the population of 2,494 respondents in grades 7–12 from a school district in Colorado to compare latent variables of self-esteem, attitudes toward school, delinquent behavior, physical injury, physical bullying, and physical victimization among 291 relational bullies, 303 victims, 213 bully-victims, and 1,687 neutrals. We used gender as a control variable. Neutrals had the best school attitudes, least problem behavior, least injury, and were less likely to be physical bullies or victims. Bully-victims reported worse outcomes on the latent variables than either neutrals or victims, and they were more likely to be physically victimized than bullies. These outcomes parallel findings among physical bullies in a similar sample. Results show the need for improved intervention, heightened awareness, and particular attention to relational bully-victims.