Journal of Iranian Statistical Society
Volume:10 Issue: 2, 2011

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property was and is well known. This paper examines the role of the scalar-parameter exponential model for obtaining approximate probabilities and approximate confidence levels, and then addresses the extension for the vector-parameter exponential model.

A common study to investigate gene-environment interaction is designed to be longitudinal and population-based. Data arising from longitudinal association studies often contain missing responses. Naive analysis without taking missingness into account may produce invalid inference, especially when the missing data mechanism depends on the response process. To address this issue in the analysis concerning gene-environment interaction effects, in this paper, we adopt an inverse probability weighted generalized estimating equations (IPWGEE) approach to conduct statistical inference. This approach is attractive because it does not require full model specification yet it can provide consistent estimates under the missing at random (MAR) mechanism. We utilize this method to analyze data arising from a cardiovascular disease study.

Variable selection via penalized estimation is appealing for dimension reduction. For penalized linear regression, Efron, et al. (2004) introduced the LARS algorithm. Recently, the coordinate descent (CD) algorithm was developed by Friedman, et al. (2007) for penalized linear regression and penalized logistic regression and was shown to gain computational superiority. This paper explores the CD algorithm to penalized Bregman divergence (BD) estimation for a broader class of models, including not only the generalized linear model, which has been well studied in the literature on penalization, but also the quasi-likelihood model, which has been less developed. Simulation study and real data application illustrate the performances of the CD and LARS algorithms in regression estimation, variable selection and classification procedure when the number of explanatory variables is large in comparison to the sample size.

The paper addresses a problem of tracking multiple number of frequencies using Regularized Autoregressive (RAR) approximation. The RAR procedure allows to decrease approximation bias, comparing to other AR-based frequency detection methods, while still providing competitive variance of sample estimates. We show that the RAR estimates of multiple periodicities are consistent in probability and illustrate dynamics of RAR in respect to sample size and signal-to-noise ration by simulations.

When using the K-nearest neighbours (KNN) method, one often ignores the uncertainty in the choice of K. To account for such uncertainty, Bayesian KNN (BKNN) has been proposed and studied (Holmes and Adams 2002; Cucala et al. 2009). We present some evidence to show that the pseudo-likelihood approach for BKNN, even after being corrected by Cucala et al. (2009), still significantly underestimates model uncertainty.

The use of mixture models for clustering and classification has burgeoned into an important subfield of multivariate analysis. These approaches have been around for a half-century or so, with significant activity in the area over the past decade. The primary focus of this paper is to review work in model-based clustering, classification, and discriminant analysis, with particular attention being paid to two techniques that can be implemented using respective R packages. Parameter estimation and model selection are also discussed. The paper concludes with a summary, discussion, and some thoughts on future work.

Variable (feature) selection has attracted much attention in contemporary statistical learning and recent scientific research. This is mainly due to the rapid advancement in modern technology that allows scientists to collect data of unprecedented size and complexity. One type of statistical problem in such applications is concerned with modeling an output variable as a function of a small subset of a large number of features. In certain applications, the data samples may even be coming from multiple subpopulations. In these cases, selecting the correct predictive features (variables) for each subpopulation is crucial. The classical best subset selection methods are computationally too expensive for many modern statistical applications. New variable selection methods have been successfully developed over the last decade to deal with large numbers of variables. They have been designed for simultaneously selecting important variables and estimating their effects in a statistical model. In this article, we present an overview of the recent developments in theory, methods, and implementations for the variable selection problem in finite mixture of regression models.

In this paper we treat a general form of location model. It is typically assumed that the error term is distributed according to the law belonging to the class of elliptically contoured distribution. Some sorts of shrinkage estimators of location and scale parameters are proposed and their exact bias and MSE expressions are derived. The performance of the estimators under study are completely analyzed and the condition of superiority of each estimator is studied in details.

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is a priori known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage method combines restricted and unrestricted estimators to obtain the parameter estimates. Such an estimator outperforms the classical maximum likelihood estimators. Any prior information may be validated through preliminary test (or pretest), and depending on the validity, may be incorporated in the model as a parametric restriction. Thus, pretest estimator chooses between the restricted and unrestricted estimators depending on the outcome of the preliminary test. Examples using three real life data sets are provided to illustrate the application of shrinkage and pretest estimation. Performance of positive-shrinkage and pretest estimators are compared with unrestricted estimator under varying degree of uncertainty of the prior information. Monte Carlo study reconfirms the asymptotic properties of the estimators available in the literature.