"Chain pooling" model selection for two-level fixed effects factorial experiments

As many as three iterated statistical model deletion procedures are considered for an experiment.Population model coeff cients were chosen to simulate a saturated 2⁴experiment having an unfavorable distribution of parameter values.Using random number studies, three model selection strategies were developed, namely, (1) a strategy to be used in anticipation of large coefficients of variation (neighborhood of 65 percent), (2) strategy to be used in anticipation of small coefficients of variation (4 percent or less), and (3) a security regret strategy to be used in the absence of such prior knowledge     

Covariate Selection for the Semiparametric Additive Risk Model

Abstract.  This paper considers covariate selection for the additive hazards model. This model is particularly simple to study theoretically and its practical implementation has several major advantages to the similar methodology for the proportional hazards model. One complication compared with the proportional model is, however, that there is no simple likelihood to work with. We here study a least squares criterion with desirable properties and show how this criterion can be interpreted as a prediction error. Given this criterion, we define ridge and Lasso estimators as well as an adaptive Lasso and study their large sample properties for the situation where the number of covariates p is smaller than the number of observations. We also show that the adaptive Lasso has the oracle property. In many practical situations, it is more relevant to tackle the situation with large p compared with the number of observations. We do this by studying the properties of the so-called Dantzig selector in the setting of the additive risk model. Specifically, we establish a bound on how close the solution is to a true sparse signal in the case where the number of covariates is large. In a simulation study, we also compare the Dantzig and adaptive Lasso for a moderate to small number of covariates. The methods are applied to a breast cancer data set with gene expression recordings and to the primary biliary cirrhosis clinical data.     

Studying the dependence between ordinal-nominal categorical variables via orthogonal polynomials

In situations where the structure of one of the variables of a contingency table is ordered recent theory involving the augmentation of singular vectors and orthogonal polynomials has shown to be applicable for performing symmetric and non-symmetric correspondence analysis. Such an approach has the advantage of allowing the user to identify the source of variation between the categories in terms of components that reflect linear, quadratic and higher-order trends. The purpose of this paper is to focus on the study of two asymmetrically related variables cross-classified to form a two-way contingency table where only one of the variables has an ordinal structure.     

Dirichlet models for square contingency tables

We consider the square contingency tables which arise when the same method of classification is applied twice. The hypothesis of marginal homogeneity is then relevant! and can be tested by various methods Models are discussed which contain marginal homogeneity as a special case. They include a class based on univariate and bivariate Dirichlet distributions. The question of ordered categories is briefly discussed. Applications are made to data on unaided distance vision.     

Bayesian Estimation of Survival Functions under Stochastic Precedence

When estimating the distributions of two random variables, X and Y, investigators often have prior information that Y tends to be bigger than X. To formalize this prior belief, one could potentially assume stochastic ordering between X and Y, which implies Pr(X < or = z) > or = Pr(Y < or = z) for all z in the domain of X and Y. Stochastic ordering is quite restrictive, though, and this article focuses instead on Bayesian estimation of the distribution functions of X and Y under the weaker stochastic precedence constraint, Pr(X < or = Y) > or = 0.5. We consider the case where both X and Y are categorical variables with common support and develop a Gibbs sampling algorithm for posterior computation. The method is then generalized to the case where X and Y are survival times. The proposed approach is illustrated using data on survival after tumor removal for patients with malignant melanoma.     

Optimal use of two auxiliary variables in double sampling

Double sampling scheme is used when cheap auxiliary variables may be measured to improve the estimation of a finite population parameter. Several estimators for population mean, ratio of means and variance are available, when two dependent samples are drawn. However, there are few proposals for the case of independent samples. In this paper both cases of dependent and independent samples are dealt with. A general approach for estimating a finite population parameter is given, showing that all the proposed estimators are particular cases of the same general class. The minimum variance bound for any estimator in this class is provided (at the first order of approximation). Furthermore, an optimal estimator which reaches this minimum is found.     

Extreme Copulas and the Comparison of Ordered Lists

We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T _M (the minimum operator) and the Ł ukasiewicz copula T _L used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of T _M and T _L two probabilistic relations Q ^M and Q ^L and identify their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods.     

康德定言命令的道德变革与实践困境

康德以纯粹理性形而上学为基础,强调善良意志和定言命令的实践理性价值.以"定言命令"为核心的道德形而上学实践理性排斥伦理学经验论,弘扬人的主体能动性,在西方伦理学引起了重大的道德哲学方向性转变.然而,"定言命令"具有形式化和僵化的普遍化特征,存在严重的形而上矛盾和现实困境,受到黑格尔等人的伦理学批判以及马克思主义唯物主义实践论的超越.     

一般信息系统的PoClustering与概念格

传统聚类方法生成的子集,一般来说都是不相交的.而严格的不相交分类结构,不能充分表现象本体这样的事物间丰富的类关系.在基因本体中,类与子类既不是简单的树也不是格结构,而是一个有向非循环图,其任何子女都可能有多个父结点.PoClustering是相异数据的一种无损聚类方法,概念格则反映了数据的对象和属性的对应关系.采用了PoClustering方法,在保持尽量多的信息的前提下建立一般数据集(信息系统)的属性确定下的概念化分类,讨论了它的算法,从概念格的角度研究了这种类的结构特征.     

Identifiable finite mixtures of location models for clustering mixed-mode data

For clustering mixed categorical and continuous data, Lawrence and Krzanowski (1996) proposed a finite mixture model in which component densities conform to the location model. In the graphical models literature the location model is known as the homogeneous Conditional Gaussian model. In this paper it is shown that their model is not identifiable without imposing additional restrictions. Specifically, for g groups and m locations, (g!)m–1 distinct sets of parameter values (not including permutations of the group mixing parameters) produce the same likelihood function. Excessive shrinkage of parameter estimates in a simulation experiment reported by Lawrence and Krzanowski (1996) is shown to be an artifact of the model's non-identifiability. Identifiable finite mixture models can be obtained by imposing restrictions on the conditional means of the continuous variables. These new identified models are assessed in simulation experiments. The conditional mean structure of the continuous variables in the restricted location mixture models is similar to that in the underlying variable mixture models proposed by Everitt (1988), but the restricted location mixture models are more computationally tractable.