A Simulation Study of the Performance of Five Discriminant Analysis Methods for Mixtures of Continuous and Binary Variables

The present study investigates the performance of fice discrimination methods for data consisting of a mixture of continuous and binary variables. The methods are Fisher’s linear discrimination, logistic discrimination, quadratic discrimination, a kernal model and an independence model. Six-dimensional data, consisting of three binary and three continuous variables, are simulated according to a location model. The results show an almost identical performance for Fisher’s linear discrimination and logistic discrimination. Only in situations with independently distributed variables the independence model does have a reasonable discriminatory ability for the dimensionality considered. If the log likelihood ratio is non-linear ratio is non-linear with respect to its continuous and binary part, the quadratic discrimination method is substantial better than linear and logistic discrimination, followed by the kernel method. A very good performance is obtained when in every situation the better one of linear and quardratic discrimination is used.     

On cross-validation for discrete kernel estimates in discrimination

The choice of smoothing determines the properties of nonparametric estimates of probability densities. In the discrimination problem, the choice is often tied to loss functions. A framework for the cross–validatory choice of smoothing parameters based on general loss functions is given. Several loss functions are considered as special cases. In particular, a family of loss functions, which is connected to discrimination problems, is directly related to measures of performance used in discrimination. Consistency results are given for a general class of loss functions which comprise this family of discriminant loss functions.     

A robust logistic discrimination model

Logistic discrimination is a well documented method for classifying observations to two or more groups. However, estimation of the discriminant rule can be seriously affected by outliers. To overcome this, Cox and Ferry produced a robust logistic discrimination technique. Although their method worked in practice, parameter estimation was sometimes prone to convergence problems. This paper proposes a simplified robust logistic model which does not have any such problems and which takes a generalized linear model form. Misclassification rates calculated in a simulation exercise are used to compare the new method with ordinary logistic discrimination. Model diagnostics are also presented. The newly proposed model is then used on data collected from pregnant women at two district general hospitals. A robust logistic discriminant is calculated which can be used to predict accurately which method of feeding a woman will eventually use: breast feeding or bottle feeding.     

Mutability of DNA base pairs: A statistical approach based on linear discrimination

A mutational spectrum measures the frequency of mutations at particular base pairs along a given DNA sequence under the influence of a particular treatment. Such spectra have been measured for several genes, in various organisms and under different treatments. This article presents a method of analysis based on the statistical discrimination between mutable base pairs and stable base pairs. The coefficients of the discriminant function characterize the mutational spectrum induced by a given treatment on a given sequence. These coefficients can be interpreted by the user without specialized statistical knowledge.     

有关距离判别理论方法的补充和讨论

距离判别理论中，通常采用重心距离来定义类与类之间的距离对待判样品进行判别。对新样品实行判别，将其归入系统聚类形成的分类，如果仍采用重心距离判别法，会由于没有与原有聚类时所用的类与类之间的距离相一致而产生误判。提出对基于系统聚类分类结果的距离判别理论方法的补充，把系统聚类中的八种类与类之间距离的概念引入到距离判别方法中。从而使距离判别中类与类距离的定义与系统聚类中相一致，通过实例分析，证明增强了距离判别的可靠性。     

On the maximum likelihood estimation of parameters of a spatial discrimination model

Consideration is given here to the problem of maximum likelihood estimation of parameters in a sparial discrimination model which was proposed by switzer (1980). some moments of these estimators are derived. These results extend the work of Mardia (1984) who gave expressions for these estimators without their moments.     

Measures of discrimination for latent group-based trajectory models

In clinical research, patient care decisions are often easier to make if patients are classified into a manageable number of groups based on homogeneous risk patterns. Investigators can use latent group-based trajectory modeling to estimate the posterior probabilities that an individual will be classified into a particular group of risk patterns. Although this method is increasingly used in clinical research, there is currently no measure that can be used to determine whether an individual's group assignment has a high level of discrimination. In this study, we propose a discrimination index and provide confidence intervals of the probability of the assigned group for each individual. We also propose a modified form of entropy to measure discrimination. The two proposed measures were applied to assess the group assignments of the longitudinal patterns of conduct disorders among young adolescent girls.     

Screening designs for model discrimination

We introduce new criteria for model discrimination and use these and existing criteria to evaluate standard orthogonal designs. We show that the capability of orthogonal designs for model discrimination is surprisingly varied. In fact, for specified sample sizes, number of factors, and model spaces, many orthogonal designs are not model discriminating by the definition given in this paper, while others in the same class of orthogonal designs are. We also use these criteria to construct optimal two-level model-discriminating designs for screening experiments. The efficacy of these designs is studied, both in terms of estimation efficiency and discrimination success. Simulation studies indicate that the constructed designs result in substantively higher likelihoods of identifying the correct model.     

Disoominkfrcn between gaussian time series based on their spectral differences

Discrimination between two Gaussian time series is examined assuming that the important difference between the alternative processes is their covarianoe (spectral) structure. Using the likelihood ratio method in frequency domain a discriminant function is derived and its approximate distribution is obtained. It is demonstrated that, utilizing the Kullbadk-Leibler information measure, the frequencies or frequency bands which carry information for discrimination can be determined. Using this, it is shown that when mean functions are equal, discrimination based on the frequency with the largest discrimination information is equivalent to the classification procedure based on the best linear discriminant, Application to seismology is described by including a discussion concerning the spectral ratio discriminant for underground nuclear explosion and natural earthquake and is illustrated numerically using Rayleigh wave data from an underground and an atmospheric explosions.     

Categorical variable selection based on entropy reduction

This paper presents the derivation of a categorical variable selection technique which utilizes the entropy function as a measure of variability for nominally scaled variables. The selection criterion uses likelihood ratio statistics which, for the hypotheses under consideration, are identical to minimum discrimination information statistics. Thus, the paper provides an alternative motivation for a selection technique based on discriminatory power, and it provides an extension of that technique to the multipopulation discrimination problem. The selection technique is illustrated for a study in which we discriminate among three populations: cervical cancer patients, population-based controls, and hospital-based controls.     

Model-based adaptive spatial sampling for occurrence map construction

In many environmental management problems, the construction of occurrence maps of species of interest is a prerequisite to their effective management. However, the construction of occurrence maps is a challenging problem because observations are often costly to obtain (thus incomplete) and noisy (thus imperfect). It is therefore critical to develop tools for designing efficient spatial sampling strategies and for addressing data uncertainty. Adaptive sampling strategies are known to be more efficient than non-adaptive strategies. Here, we develop a model-based adaptive spatial sampling method for the construction of occurrence maps. We apply the method to estimate the occurrence of one of the world’s worst invasive species, the red imported fire ant, in and around the city of Brisbane, Australia. Our contribution is threefold: (i) a model of uncertainty about invasion maps using the classical image analysis probabilistic framework of Hidden Markov Random Fields (HMRF), (ii) an original exact method for optimal spatial sampling with HMRF and approximate solution algorithms for this problem, both in the static and adaptive sampling cases, (iii) an empirical evaluation of these methods on simulated problems inspired by the fire ants case study. Our analysis demonstrates that the adaptive strategy can lead to substantial improvement in occurrence mapping.     

教育回报率的性别差异研究

利用CHNS2006中的成年人数据,运用Oaxaca-Blinder分解方法,对男女工资收人分解后的系数差异进行了经验检验.研究结果表明:提高女性受教育程度可以确实有效地降低劳动力市场上的性别歧视.     

Bayesian incorporation of repeated measurements in logistic discrimination

A common problem in medical statistics is the discrimination between two groups on the basis of diagnostic information. Information on patient characteristics is used to classify individuals into one of two groups: diseased or disease-free. This classification is often with respect to a particular disease. This discrimination has two probabilistic components: (1) the discrimination is not without error, and (2) in many cases the a priori chance of disease can be estimated. Logistic models (Cox 1970; Anderson 1972) provide methods for incorporating both of these components. The a posteriori probability of disease may be estimated for a patient on the basis of both current measurement of patient characteristics and prior information. The parameters of the logistic model may be estimated on the basis of a calibration trial. In practice, not one but several sets of measurements of one characteristic of the patient may be made on a questionable case. These measurements typically are correlated; they are far from independent. How should these correlated measurements be used? This paper presents a method for incorporating several sets of measurements in the classification of a case.     

Bivariate deconvolution with SIMEX: an application to mapping Alaska earthquake density

Constructing spatial density maps of seismic events, such as earthquake hypocentres, is complicated by the fact that events are not located precisely. In this paper, we present a method for estimating density maps from event locations that are measured with error. The estimator is based on the simulation–extrapolation method of estimation and is appropriate for location errors that are either homoscedastic or heteroscedastic. A simulation study shows that the estimator outperforms the standard estimator of density that ignores location errors in the data, even when location errors are spatially dependent. We apply our method to construct an estimated density map of earthquake hypocenters using data from the Alaska earthquake catalogue.     

An extension of geisser's discrimination model to proportional covariance matrices

The predictive discrimination model of Geisser is derived for the case in which the covariance matrices of the different populations are assumed proportional, with unknown constants of proportionality. It is shown that this model provides a better fit to a set of data than does the usual homoscedastic model.     

Renyi entropy properties of mixed systems

This paper deals with Renyi information properties of mixed systems when lifetimes of components are independent and identically distributed. The provided results are obtained by using the concept of Samaniego’s signature. Stochastic comparisons of Renyi entropy for mixed systems are discussed provided that both systems have the same signature. To approximate the behavior of the Renyi entropy, some bounds are also given. In the rest, Renyi discrimination information between the distribution of system’s lifetime and component lifetime are obtained and proved that they are distribution free and depends only on the system signature.     

Multivariate thin plate spline estimates for the posterior probabilities in the classification problem

A nonparametric estimate for the posterior probabilities in the classification problem using multivariate thin plate splines is proposed. This method presents a nonpararnetric alternative to logistic discrimination as well as to survival curve estimation. The degree of smoothness of the estimate is determined from the data using generalized crossvalidation.     

Parametric scalp mapping and inference via spatially smooth linear models for mismatch negativity studies

Mismatch negativity (MMN) is a neurophysiological tool that can be used to investigate various facets of comprehension. Subjects are presented with different stimuli to elicit the MMN response, which is derived from electroencephalography (EEG) signals recorded at electrodes across the brain. We propose a methodology to extend single electrode analyses of MMN data by generating smooth scalp maps of estimated experimental effects. It is shown that penalized least squares estimates of effect maps can be produced using a two step procedure involving (a) ANOVA at each electrode and (b) spatial smoothing across electrodes. A Fisher von-Mises kernel is used for smoothing scalp maps with cross-validated bandwidth selection. The methodology is applied to a case control study involving aphasics (language disordered individuals). Analysis of residuals shows possible heteroscedasticity and non-Gaussian tail behavior. For robust inference, a semiparametric multivariate approach is proposed to determine the significance of parametric maps. A variety of global and regional test statistics are developed to investigate the significance of spatial patterns in treatment effects. The methodology is seen to confirm previous findings from single electrode analysis and identifies some new significant spatial patterns of difference between controls and aphasics.     

Discrimination Measures for Fractional Integrated Models Based on Wavelets

Discrimination measures have been well developed for stationary time series. However in a large number of phenomena, long-term dependencies are involved. In this article, we are dealing with discrimination of fractional integrated models. Kullback–Leibler and Chernoff's discrimination measures are approximated, using the discrete wavelet transform (DWT) for discrimination of these time series classes. The simulation study indicates low misclassification rate, related to the approximations of Kullback–Leibler and Chernoff discrimination measures. Application to problem of classifying seismic data showed that our procedure performs as well as other procedures.     

Discriminating between distributions using feed-forward neural networks

A relevant problem in many applicatory contexts is to test whether some given observations follow one of two possible probability distributions. The vast literature produced over the years on this topic does not identify a tool which can be easily adopted to any situation but only finds solutions to specific comparisons. Recently, an easy to implement procedure for discrimination between two distributions based on feed-forward neural networks has been proposed giving interesting results. In this work this procedure is further investigated in terms of power, neural network architecture and expected statistical properties of the test statistic for small, moderate and large sample sizes, in a wide range of symmetric and skewed alternatives.