Block and Basu bivariate lifetime distribution in the presence of cure fraction

This paper presents estimates for the parameters included in the Block and Basu bivariate lifetime distributions in the presence of covariates and cure fraction, applied to analyze survival data when some individuals may never experience the event of interest and two lifetimes are associated with each unit. A Bayesian procedure is used to get point and confidence intervals for the unknown parameters. Posterior summaries of interest are obtained using standard Markov Chain Monte Carlo methods in rjags package for R software. An illustration of the proposed methodology is given for a Diabetic Retinopathy Study data set.     

Identifying radon-prone building typologies by marginal modelling

Radon is a naturally occurring decay product of uranium known to be the main contributor to natural background radiation exposure. It has been established that the health risk related to radon exposure is lung cancer. In fact, radon is considered to be a major leading cause of lung cancer, second only to smoking. In this paper, we identified building typologies that affect the probability of detecting indoor radon concentration above reference values, using the data collected within two monitoring campaigns recently conducted in Northern Italy. This information is fundamental both in prevention, i.e. when the construction of a new building is planned and in mitigation, i.e. when a high concentration detected inside buildings has to be reduced. A spatial regression approach for binary data was adopted for this goal where some relevant covariates on the soil were retrieved by linking external spatial databases.     

Asymptotic normality of Huber–Dutter estimators in a linear model with AR(1) processes

The paper studies a linear regression model with first order autoregressive (AR(1)) processes. The Huber–Dutter (HD) estimators of unknown parameters are given, and the asymptotic normality of the HD estimators is investigated. An example is presented to illustrate the proposed method.     

Simultaneous Confidence Regions for Predictions

After observing n independent responses at n corresponding design points in a linear regression setting, one wishes to make a confidence statement about future responses that will apply simultaneously to all possible design points. Two appropriate prediction regions are derived using normal theory.     

Frequency of Selecting Noise Variables in Subset Regression Analysis: A Simulation Study

This article presents the results of a simulation study of variable selection in a multiple regression context that evaluates the frequency of selecting noise variables and the bias of the adjusted R ² of the selected variables when some of the candidate variables are authentic. It is demonstrated that for most samples a large percentage of the selected variables is noise, particularly when the number of candidate variables is large relative to the number of observations. The adjusted R ² of the selected variables is highly inflated.     

Hierarchical Variable Selection in Polynomial Regression Models

Significance tests on coefficients of lower-order terms in polynomial regression models are affected by linear transformations. For this reason, a polynomial regression model that excludes hierarchically inferior predictors (i.e., lower-order terms) is considered to be not well formulated. Existing variable-selection algorithms do not take into account the hierarchy of predictors and often select as “best” a model that is not hierarchically well formulated. This article proposes a theory of the hierarchical ordering of the predictors of an arbitrary polynomial regression model in m variables, where m is any arbitrary positive integer. Ways of modifying existing algorithms to restrict their search to well-formulated models are suggested. An algorithm that generates all possible well-formulated models is presented.     

Interpreting an Inequality in Multiple Regression

This article provides a method of interpreting a surprising inequality in multiple linear regression: the squared multiple correlation can be greater than the sum of the simple squared correlations between the response variable and each of the predictor variables. The interpretation is obtained via principal component analysis by studying the influence of some components with small variance on the response variable. One example is used as an illustration and some conclusions are derived.     

Bayesian Binomial Regression: Predicting Survival at a Trauma Center

Standard methods for analyzing binomial regression data rely on asymptotic inferences. Bayesian methods can be performed using simple computations, and they apply for any sample size. We provide a relatively complete discussion of Bayesian inferences for binomial regression with emphasis on inferences for the probability of “success.” Furthermore, we illustrate diagnostic tools, perform model selection among nonnested models, and examine the sensitivity of the Bayesian methods.     

On a Relation between Principal Components and Regression Analysis

A regression approach to principal component analysis is presented in this note. We provide an alternative interpretation of principal components that illustrates the relation between the extra sum of squares in regression analysis and the eigenvalues associated with the principal components.     

Functional sliced inverse regression analysis

Most of the usual multivariate methods have been extended to the context of functional data analysis. Our contribution concerns the study of sliced inverse regression (SIR) when the response variable is real but the regressor is a function. In the first part, we show how the relevant properties of SIR remain essentially the same in the functional context under suitable conditions. Unfortunately, the estimation procedure used in the multivariate case cannot be directly transposed to the functional one. Then, we propose a solution that overcomes this difficulty and we show the consistency of the estimates of the parameters of the model.