A Partial Likelihood Estimator of Vaccine Efficacy

A partial likelihood method is proposed for estimating vaccine efficacy for a general epidemic model. In contrast to the maximum likelihood estimator (MLE) which requires complete observation of the epidemic, the suggested method only requires information on the sequence in which individuals are infected and not the exact infection times. A simulation study shows that the method performs almost as well as the MLE. The method is applied to data on the infectious disease mumps.     

Semiparametric estimation of spatial long-range dependence

Estimation of the long-range dependence parameter in spatial processes using a semiparametric approach is studied. An extended formulation of the averaged periodogram method proposed in Robinson [1994. Semiparametric analysis of long memory time series. Ann. Statist. 22, 515–539] is derived, considering a certain homogeneous and isotropic behaviour of the spectral distribution in the low frequencies. The weak consistency of the estimator proposed is proved.     

Bayesian optimal design for changepoint problems

We investigate Bayesian optimal designs for changepoint problems. We find robust optimal designs which allow for arbitrary distributions before and after the change, arbitrary prior densities on the parameters before and after the change, and any log‐concave prior density on the changepoint. We define a new design measure for Bayesian optimal design problems as a means of finding the optimal design. Our results apply to any design criterion function concave in the design measure. We illustrate our results by finding the optimal design in a problem motivated by a previous clinical trial. The Canadian Journal of Statistics 37: 495–513; 2009 © 2009 Statistical Society of Canada     

Semiparametric estimation of employment duration models

There are a variety of economic areas, such as studies of employment duration and of the durability of capital goods, in which data on important variables typically are censored. The standard techinques for estimating a model from censored data require the distributions of unobservable random components of the model to be specified a priori up to a finite set of parameters, and misspecification of these distributions usually leads to inconsistent parameter estimates. However, economic theory rarely gives guidance about distributions and the standard estimation techniques do not provide convenient methods for identifying distributions from censored data. Recently, several distribution-free or semiparametric methods for estimating censored regression models have been developed. This paper presents the results of using two such methods to estimate a model of employment duration. The paper reports the operating characteristics of the semiparametric estimators and compares the semiparametric estimates with those obtained from a standard parametric model.     

Weak Convergence of the Regularization Path in Penalized M‐Estimation

Abstract. We consider a function defined as the pointwise minimization of a doubly index random process. We are interested in the weak convergence of the minimizer in the space of bounded functions. Such convergence results can be applied in the context of penalized M‐estimation, that is, when the random process to minimize is expressed as a goodness‐of‐fit term plus a penalty term multiplied by a penalty weight. This weight is called the regularization parameter and the minimizing function the regularization path. The regularization path can be seen as a collection of estimators indexed by the regularization parameter. We obtain a consistency result and a central limit theorem for the regularization path in a functional sense. Various examples are provided, including the ?¹‐regularization path for general linear models, the ?¹‐ or ?²‐regularization path of the least absolute deviation regression and the Akaike information criterion.     

Inclusion of Dietary Evaluation in Cardiovascular Disease Risk Prediction Models Increases Accuracy and Reduces Bias of the Estimations

In the past few years, the prediction of CVD risk has received special attention; however, some investigators assert that risk models have so far not been very successful. Thus, we examined whether the inclusion of dietary evaluation in a risk prediction model that already contained the classical CVD risk factors increases the accuracy and reduces the bias in estimating future CVD events. The database of the ATTICA study (which included information from 1,514 men and 1,528 women) was used. At baseline, the HellenicSCORE values (based on age, gender, smoking, systolic blood pressure, and total cholesterol) were calculated, while overall assessment of dietary habits was based on the Mediterranean diet score (MDS) that evaluates adherence to this traditional diet. In 2006, a five-year follow-up was performed in 2,101 participants and development of CVD (coronary heart disease, acute coronary syndromes, stroke, or other CVD) was defined according to WHO-ICD-10 criteria. The MDS and the HellenicSCORE were significant predictors of CVD events, even after adjusting for various potential confounders ( p < 0.05). However, estimating bias (i.e., misclassification of cases) of the model that included HellenicSCORE and other potential confounders was 8.7%. The MDS was associated with the estimating bias of the outcome ( p < 0.001) and explained 5.5% of this bias. Other baseline factors associated with bias were increased body mass index, low education status, and increased energy intake/BMR ratio. The inclusion of dietary evaluation, as well as other Sociodemographic and anthropometric characteristics, increases the accuracy and reduces estimating bias of CVD risk prediction models.     

A design-based randomized response procedure for the estimation of population proportion and sensitivity level

A general design-based approach to randomized response surveys is proposed. The method is tailored for the joint estimation of the proportion of individuals in the population bearing a sensitive attribute and the proportion of individuals in the sensitive group declaring truthfully their status. The proposal is specialized to the case of simple random sampling without replacement, unequal probability sampling without replacement and stratified sampling.     

Delay Estimation for Some Stationary Diffusion-type Processes

In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation with one time delay term. It is shown that these estimators are consistent and their limit distributions are described. The behaviour of the estimators is similar to the behaviour of corresponding estimators in change-point problems. The question of asymptotical efficiency is also discussed.     

Estimation of Pr(Y < X) for the two-parameter generalized exponential records

This article considers the maximum likelihood and Bayes estimation of the stress–strength reliability based on two-parameter generalized exponential records. Here, we extend the results of Baklizi [Computational Statistics and Data Analysis 52 (2008), 3468–3473] to explain a wide variety of real datasets. We also consider the estimation of R when the same shape parameter is known. The results for exponential distribution can be obtained as a special case with different scale parameters.