Covariate selection for estimating the causal effect of control plans by using causal diagrams

Summary. Consider a case where cause–effect relationships between variables can be described by a causal path diagram and the corresponding linear structural equation model. The paper proposes a graphical selection criterion for covariates to estimate the causal effect of a control plan. For designing the control plan, it is essential to determine both covariates that are used for control and covariates that are used for identification. The selection of covariates used for control is only constrained by the requirement that the covariates be non-descendants of a treatment variable. However, the selection of covariates used for identification is dependent on the selection of covariates used for control and is not unique. In the paper, the difference between covariates that are used for identification is evaluated on the basis of the asymptotic variance of the estimated causal effect of an effective control plan. Furthermore, the results can be also described in terms of a graph structure.     

Minimum variance rectangular designs for U-statistics

We consider a certain class of rectangular designs for incomplete U-statistics based on Latin squares and show it to be optimal with respect to the minimal variance criterion. We also show it to be asymptotically efficient when compared with the corresponding complete statistics, as well as uniformly more efficient than the random subset selection. We provide the necessary and sufficient conditions for the existence of our design and give some examples of applications.     

Prediction in linear mixed models

Following estimation of effects from a linear mixed model, it is often useful to form predicted values for certain factor/variate combinations. The process has been well defined for linear models, but the introduction of random effects into the model means that a decision has to be made about the inclusion or exclusion of random model terms from the predictions. This paper discusses the interpretation of predictions formed including or excluding random terms. Four datasets are used to illustrate circumstances where different prediction strategies may be appropriate: in an orthogonal design, an unbalanced nested structure, a model with cubic smoothing spline terms and for kriging after spatial analysis. The examples also show the need for different weighting schemes that recognize nesting and aliasing during prediction, and the necessity of being able to detect inestimable predictions.     

The role of reversals in order‐restricted inference

A statistical model is said to be an order‐restricted statistical model when its parameter takes its values in a closed convex cone C of the Euclidean space. In recent years, order‐restricted likelihood ratio tests and maximum likelihood estimators have been criticized on the grounds that they may violate a cone order monotonicity (COM) property, and hence reverse the cone order induced by C. The authors argue here that these reversals occur only in the case that C is an obtuse cone, and that in this case COM is an inappropriate requirement for likelihood‐based estimates and tests. They conclude that these procedures thus remain perfectly reasonable procedures for order‐restricted inference.     

一个离散数学问题

本文将一个数学竞赛题的证明,归结为整数变量的多元平方和函数的最小值问题的求解,这些变量的和等于一个整数常数,这样的函数的最小值,及最大值的问题,则是更重要的离散数学问题,本文对此问题的求解,建立了完整的理论,并给出了一般的解法。     

高速公路隧道施工过程的新奥法监控

结合中梁山隧道西段施工现场的实测数据,分析了该段围岩变形的条件和规律,并对各类围岩的各测线进行了量测数据回归分析,导出了各类围岩的稳定性判据,给出了最佳初期支护及二次衬砌时间。     

Simulations on the Jelinski-Moranda model of software reliability; application of some parametric bootstrap methods

In software reliability theory many different models have been proposed and investigated. some of these models intuitively match reality better than others. The properties of certain statistical estimation procedures in connection with these models are also model-dependent. In this paper we investigate how well the maximum likelihood estimation procedure and the parametric bootstrap behave in the case of the very well-known software reliability model suggested by Jelinski and Moranda (1972). For this study we will make use of simulated data.     

THE CUBE OF A LOGISTIC DISTRIBUTION IS INDETERMINATE

It is known that most distributions are uniquely determined by their moments. Exceptions exist, but are believed to be rare among those we encounter in everyday life applications. We add one more to the rare collection, and suggest that indeterminate distributions are perhaps more prevalent than is commonly perceived.     

Mixture separation for mixed-mode data

One possible approach to cluster analysis is the mixture maximum likelihood method, in which the data to be clustered are assumed to come from a finite mixture of populations. The method has been well developed, and much used, for the case of multivariate normal populations. Practical applications, however, often involve mixtures of categorical and continuous variables. Everitt (1988) and Everitt and Merette (1990) recently extended the normal model to deal with such data by incorporating the use of thresholds for the categorical variables. The computations involved in this model are so extensive, however, that it is only feasible for data containing very few categorical variables. In the present paper we consider an alternative model, known as the homogeneous Conditional Gaussian model in graphical modelling and as the location model in discriminant analysis. We extend this model to the finite mixture situation, obtain maximum likelihood estimates for the population parameters, and show that computation is feasible for an arbitrary number of variables. Some data sets are clustered by this method, and a small simulation study demonstrates characteristics of its performance.     

Nonparametric estimation of renewal processes from count data

Abstract: The authors address the problem of estimating an inter‐event distribution on the basis of count data. They derive a nonparametric maximum likelihood estimate of the inter‐event distribution utilizing the EM algorithm both in the case of an ordinary renewal process and in the case of an equilibrium renewal process. In the latter case, the iterative estimation procedure follows the basic scheme proposed by Vardi for estimating an inter‐event distribution on the basis of time‐interval data; it combines the outputs of the E‐step corresponding to the inter‐event distribution and to the length‐biased distribution. The authors also investigate a penalized likelihood approach to provide the proposed estimation procedure with regularization capabilities. They evaluate the practical estimation procedure using simulated count data and apply it to real count data representing the elongation of coffee‐tree leafy axes.