Gaussian copula distributions for mixed data,with application in discrimination

The construction of a joint model for mixed discrete and continuous random variables that accounts for their associations is an important statistical problem in many practical applications. In this paper, we use copulas to construct a class of joint distributions of mixed discrete and continuous random variables. In particular, we employ the Gaussian copula to generate joint distributions for mixed variables. Examples include the robit-normal and probit-normal-exponential distributions, the first for modelling the distribution of mixed binary-continuous data and the second for a mixture of continuous, binary and trichotomous variables. The new class of joint distributions is general enough to include many mixed-data models currently available. We study properties of the distributions and outline likelihood estimation; a small simulation study is used to investigate the finite-sample properties of estimates obtained by full and pairwise likelihood methods. Finally, we present an application to discriminant analysis of multiple correlated binary and continuous data from a study involving advanced breast cancer patients.     

Tests for Equality of Parameters of Two Exponential Distributions with Common Known Coefficient of Variation

ABSTRACT

This article considers the problem of testing equality of parameters of two exponential distributions having common known coefficient of variation, both under unconditional and conditional setup. Unconditional tests based on BLUE'S and LRT are considered. Using the Conditionality Principle of Fisher, an UMP conditional test for one-sided alternative is derived by conditioning on an ancillary. This test is seen to be uniformly more powerful than unconditional tests in certain given ranges of ancillary. Simulation studies on the power functions of the tests are done for this purpose.     

化学热力学函数偏微商等式证明方法探讨

从基础热力学函数的相互关系出发，结合偏微商运算基本原理，归纳热力学函数偏微商变换的常用途径，并对化学热力学函数偏微商式的证明方法及技巧进行一些具体研讨。     

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.     

Alternate test statistics for a functional errors-in-variables model

Some test statistics for the structural coefficients of simultaneous equations model often referred to as the multivariate linear functional relationship model are proposed in this article. The following cases are considered: the covariance matrix of errors is either unknown, known up to a proportionality factor, or completely known. The exact and approximate distributions of the proposed test statistics, as well as those of some that are known, are also given.     

Risk of Extreme Events in Multiobjective Decision Trees Part 1. Severe Events

Earlier work with decision trees identified nonseparability as an obstacle to minimizing the conditional expected value, a measure of the risk of extreme events, by the well-known method of averaging out and folding back. This first of two companion papers addresses the conditional expected value that is defined as the expected outcome assuming the exceedance of a threshold β, where β is preselected by the decision maker. An approach is proposed to overcome the need to evaluate all policies in order to identify the optimal policy. The approach is based on the insight that the conditional expected value is separable into two constituent elements of risk and can thus be optimized along with other objectives, including the unconditional expected value of the outcome, by using a multiobjective decision tree. An example of sequential decision making for improving highway capacity is given.     

条件绝对转移指令与条件相对转移指令

本文主要对条件绝对转移指令与条件相对转移指令的使用范围进行分析并举例说明.     

Seasonal Time Series and Transfer Function Modeling

A simple modification is suggested for the construction of transfer function models relating an output variable Y_t to an input variable X_t when the model for X_t contains operators that cancel out. In addition, the evaluation of transfer function models is discussed by comparing the forecasts with the actual observations.     

Infinite Parameter Estimates in Logistic Regression, with Application to Approximate Conditional Inference

This paper discusses recovery of information regarding logistic regression parameters in cases when maximum likelihood estimates of some parameters are infinite. An algorithm for detecting such cases and characterizing the divergence of the parameter estimates is presented. A method for fitting the remaining parameters is also presented . All of these methods rely only on sufficient statistics rather than less aggregated quantities, as required for inference according to the method of Kolassa & Tanner (1994). These results are applied to approximate conditional inference via saddlepoint methods. Specifically, the double saddlepoint method of Skovgaard (1987) is adapted to the case when the solution to the saddlepoint equations exists as a point at infinity     

Multiobjective Decision-Tree Analysis1

Single-objective-based decision-tree analysis has been extensively and successfully used in numerous decision-making problems since its formal introduction by Howard Raiffa more than two decades ago. This paper extends the traditional methodology to incorporate multiple noncommensurate objective functions and use of the conditional expected value of the risk of extreme and catastrophic events. The proposed methodology considers the cases where (a) a finite number of actions are available at each decision node and (b) discrete or continuous states of nature can be presented at each chance node. The proposed extension of decision-tree analysis is introduced through an example problem that leads the reader step-by-step into the methodological procedure. The example problem builds on flood warning systems. Two noncommensurate objectives—the loss of lives and the loss of property (including monetary costs of the flood warning system)–are incorporated into the decision tree. In addition, two risk measures—the common expected value and the conditional expected value of extreme and catastrophic events—are quantified and are also incorporated into the decision-making process. Theoretical difficulties associated with the stage-wise calculation of conditional expected values are identified and certain simplifying assumptions are made for computational tractibility. In particular, it is revealed that decisions concerning experimentation have a very interesting impact on the noninferior solution set of options—a phenomenon that has no equivalence in the single-objective case.