Stanley L. Sclove

Application of model-selection criteria to some problems in multivariate analysis

A review of model-selection criteria is presented, with a view toward showing their similarities. It is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model-selection criteria. Consideration is given to application of model-selection criteria to some problems of multivariate analysis, especially the clustering of variables, factor analysis and, more generally, describing a complex of variables.

Improved Estimators for Coefficients in Linear Regression

Point estimators for the coefficients in orthogonal linear regression which are better than the ordinary least squares estimator are obtained when at least three coefficients are to be estimated. The measure of goodness of an estimator is the sum, or weighted sum, of the componentwise mean squared errors. Some of the new estimators have interpretations as estimators which depend upon preliminary tests of significance. These estimators may be especially appropriate when the independent variables fall into two sets or are ordered, as in polynomial regression or regression on principal components. The extension of the results to the general case of nonorthogonal regression is given; here the measure of goodness of an estimator is the mean of a quadratic form in the componentwise errors.

Application of the Conditional Population-Mixture Model to Image Segmentation

The problem of image segmentation is considered in the context of a mixture of probability distributions. The segments fall into classes. A probability distribution is associated with each class of segment. Parametric families of distributions are considered, a set of parameter values being associated with each class. With each observation is associated an unobservable label, indicating from which class the observation arose. Segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function. A numerical example is given. Choice of the number of classes, using Akaikes information criterion (AIC) for model identification, is illustrated.

Multi-Sample Cluster Analysis Using Akaike's Information Criterion.

SummaryMulti-sample cluster analysis, the problem of grouping samples, is studied from an information-theoretic viewpoint via Akaikes Information Criterion (AIC). This criterion combines the maximum value of the likelihood with the number of parameters used in achieving that value. The multi-sample cluster problem is defined, and AIC is developed for this problem. The form of AIC is derived in both the multivariate analysis of variance (MANOVA) model and in the multivariate model with varying mean vectors and variance-covariance matrices. Numerical examples are presented for AIC and another criterion calledw-square. The results demonstrate the utility of AIC in identifying the best clustering alternatives.

Evaluating A Multiple‐Family Group Access Intervention for Refugees with PTSD

The purpose of this study was to analyze the effects of a multiple-family group in increasing access to mental health services for refugees with posttraumatic stress disorder (PTSD). This study investigated a nine-session multiple-family group called Coffee and Families Education and Support with refugee families from Bosnia-Herzegovina in Chicago. Adults with PTSD (n = 197) and their families were randomly assigned to receive either the intervention or a control condition. The results indicated that a multiple-family group was effective in increasing access to mental health services and that depression and family comfort with discussing trauma mediated the intervention effect. Further well-designed studies of family interventions are needed for developing evidence-based interventions for refugee families.

Data mining on time series: an illustration using fast-food restaurant franchise data

Abstract Given the widespread use of modern information technology, a large number of time series may be collected during normal business operations. We use a fast-food restaurant franchise as a case to illustrate how data mining can be applied to such time series, and help the franchise reap the benefits of such an effort. Time series data mining at both the store level and corporate level are discussed. Box–Jenkins seasonal ARIMA models are employed to analyze and forecast the time series. Instead of a traditional manual approach of Box–Jenkins modeling, an automatic time series modeling procedure is employed to analyze a large number of highly periodic time series. In addition, an automatic outlier detection and adjustment procedure is used for both model estimation and forecasting. The improvement in forecast performance due to outlier adjustment is demonstrated. Adjustment of forecasts based on stored historical estimates of like-events is also discussed. Outlier detection also leads to information that can be used not only for better inventory management and planning, but also to identify potential sales opportunities. To illustrate the feasibility and simplicity of the above automatic procedures for time series data mining, the SCA Statistical System is employed to perform the related analysis.

Development of a Mathematical Formula for the Calculation of Fingerprint Probabilities Based on Individual Characteristics

Abstract A method is developed for assigning a probability to a fingerprint, including a partial print, based on the number of individual (Galton) characteristics present. A multinomial model is used, the categories of which are the individual characteristics and combinations of them. The negative of the logarithm of the probability of any particular configuration is related to the entropy function of information theory. The parameters of the model are estimated from data (fingerprints). Confidence bounds are obtained for the negative log probability of any configuration.

Time-series segmentation: A model and a method

Abstract The problem of partitioning time series into segments is treated. The segments are considered as falling into classes. A different probability distribution is associated with each class of segment. Parametric families of distributions are considered, a set of parameter values being associated with each class. With each observation is associated an unobservable label, indicating from which class the observation arose. The label process is modeled as a Markov chain. Segmentation algorithms are obtained by applying a relaxation method to maximize the resulting likelihood function. Special attention is given to the situation in which the observations are conditionally independent, given the labels. A numerical example, segmentation of the U.S. gross national product, is given. Choice of the number of classes, using statistical model selection criteria, is illustrated.

The Occurrence of Fingerprint Characteristics as a Two-Dimensional Process

Abstract Osterburg, Parthasarathy, Raghavan, and Sclove (1977) developed a model for assigning a probability to a fingerprint, including a partial print, based on the number of Galton characteristics (ridge endings, forks, etc.) present. A grid of 1-mm squares was placed over a fingerprint. A multinomial model for the cells of the grid was used, the categories being the individual characteristics and combinations of them. In the present article this model is extended to consider dependence among the cells of the grid. The occurrence of the characteristics is modeled as a two-dimensional Markov-type process.

Population mixture models and clustering algorithms

The problem of clustering individuals is considered within the context of a mixture of distributions. A modification of the usual approach to population mixtures is employed. As usual, a parametric family of distributions is considered, a set of parameter values being associated with each population. In addition, with each observation is associated an identification parameter, Indicating from which population the observation arose. Theresulting likelihood function is interpreted in terms of the conditional probability density of a sample from a mixture of populations, given the identification parameter of each observation. Clustering algorithms are obtained by applying a method of iterated maximum likelihood to this like-lihood function.