A test for abrupt change in hazard regression models with Weibull baselines

We develop a likelihood ratio test for an abrupt change point in Weibull hazard functions with covariates, including the two-piece constant hazard as a special case. We first define the log-likelihood ratio test statistic as the supremum of the profile log-likelihood ratio process over the interval which may contain an unknown change point. Using local asymptotic normality (LAN) and empirical measure, we show that the profile log-likelihood ratio process converges weakly to a quadratic form of Gaussian processes. We determine the critical values of the test and discuss how the test can be used for model selection. We also illustrate the method using the Chronic Granulomatous Disease (CGD) data.     

Robust estimation for ordinal regression

Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.     

Two tests for sequential detection of a change-point in a nonlinear model

In this paper, two tests, based on weighted CUSUM of the least squares residuals, are studied to detect in real time a change-point in a nonlinear model. A first test statistic is proposed by extension of a method already used in the literature but for the linear models. It is tested under the null hypothesis, at each sequential observation, that there is no change in the model against a change presence. The asymptotic distribution of the test statistic under the null hypothesis is given and its convergence in probability to infinity is proved when a change occurs. These results will allow to build an asymptotic critical region. Next, in order to decrease the type I error probability, a bootstrapped critical value is proposed and a modified test is studied in a similar way. A generalization of the Hájek–Rényi inequality is established.     

Fast and Accurate Inference for the Smoothing Parameter in Semiparametric Models

A fast and accurate method of confidence interval construction for the smoothing parameter in penalised spline and partially linear models is proposed. The method is akin to a parametric percentile bootstrap where Monte Carlo simulation is replaced by saddlepoint approximation, and can therefore be viewed as an approximate bootstrap. It is applicable in a quite general setting, requiring only that the underlying estimator be the root of an estimating equation that is a quadratic form in normal random variables. This is the case under a variety of optimality criteria such as those commonly denoted by maximum likelihood (ML), restricted ML (REML), generalized cross validation (GCV) and Akaike's information criteria (AIC). Simulation studies reveal that under the ML and REML criteria, the method delivers a near‐exact performance with computational speeds that are an order of magnitude faster than existing exact methods, and two orders of magnitude faster than a classical bootstrap. Perhaps most importantly, the proposed method also offers a computationally feasible alternative when no known exact or asymptotic methods exist, e.g. GCV and AIC. An application is illustrated by applying the methodology to well‐known fossil data. Giving a range of plausible smoothed values in this instance can help answer questions about the statistical significance of apparent features in the data.     

On the recoding of continuous and bounded indexes to a binomial form: an application to quality-of-life scores

The statistical analysis of patient-reported outcomes (PROs) as endpoints has shown to be of great practical relevance. The resulting scores or indexes from the questionnaires used to measure PROs could be treated as continuous or ordinal. The goal of this study is to propose and evaluate a recoding process of the scores, so that they can be treated as binomial outcomes and, therefore, analyzed using logistic regression with random effects. The general methodology of recoding is based on the observable values of the scores. In order to obtain an optimal recoding, the evaluation of the recoding method is tested for different values of the parameters of the binomial distribution and different probability distributions of the random effects. We illustrate, evaluate and validate the proposed method of recoding with the Short Form-36 (SF-36) Survey and real data. The optimal recoding approach is very useful and flexible. Moreover, it has a natural interpretation, not only for ordinal scores, but also for questionnaires with many dimensions and different profiles, where a common method of analysis is desired, such as the SF-36.     

Multivariate linear regression for heterogeneous data

The problem of multivariate regression modelling in the presence of heterogeneous data is dealt to address the relevant issue of the influence of such heterogeneity in assessing the linear relations between responses and explanatory variables. In spite of its popularity, clusterwise regression is not designed to identify the linear relationships within ‘homogeneous’ clusters exhibiting internal cohesion and external separation. A within-clusterwise regression is introduced to achieve this aim and, since the possible presence of a linear relation ‘between’ clusters should be also taken into account, a general regression model is introduced to account for both the between-cluster and the within-cluster regression variation. Some decompositions of the variance of the responses accounted for are also given, the least-squares estimation of the parameters is derived, together with an appropriate coordinate descent algorithms and the performance of the proposed methodology is evaluated in different datasets.     

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.