Gianfranco Adimari

Empirical Likelihood Type Confidence Intervals Under Random Censorship

In this paper a simple way to obtain empirical likelihood type confidenceintervals for the mean under random censorship is suggested. An extension tothe more general case where the functional of interest is an M-functional isdiscussed and the proposed technique is used to construct confidenceintervals for quantiles. The results of a simulation study carried out toassess the accuracy of these inferential procedures are also given.

Robust inference for generalized linear models with application to logistic regression

In this paper we consider a suitable scale adjustment of the estimating function which defines a class of robust M-estimators for generalized linear models. This leads to a robust version of the quasi-profile loglikelihood which allows us to derive robust likelihood ratio type tests for inference and model selection having the standard asymptotic behaviour. An application to logistic regression is discussed.

Quasi-Profile Log Likelihoods for Unbiased Estimating Functions

This paper presents a new quasi-profile loglikelihood with the standard kind of distributional limit behaviour, for inference about an arbitrary one-dimensional parameter of interest, based on unbiased estimating functions. The new function is obtained by requiring the corresponding quasi-profile score function to have bias and information bias of order O(1). We illustrate the use of the proposed pseudo-likelihood with an application to robust inference in linear models.

Partially parametric interval estimation of Pr{Y>X}

Let X and Y be two independent continuous random variables. Three techniques to obtain confidence intervals for @r=Pr{Y>X} are discussed in a partially parametric framework. One method relies on the asymptotic normality of an estimator for @r; the remaining methods involve empirical likelihood and combine it with maximum likelihood estimation and with full parametric likelihood, respectively. Finite-sample accuracy of the confidence intervals is assessed through a simulation study. An illustration is given using a data set on the detection of carriers of Duchenne Muscular Dystrophy.

An empirical likelihood statistic for quantiles

In this paper a new version of the empirical log-likelihood ratio function for quantiles is presented. It is based on a suitable smooth version of the usual empirical distribution function and yields confidence intervals which are simple to compute and very accurate, even in small samples.

Quasi-likelihood fromM-estimators: A numerical comparison with empirical likelihood

In this paper we compare two robust pseudo-likelihoods for a parameter of interest, also in the presence of nuisance parameters. These functions are obtained by computing quasi-likelihood and empirical likelihood from the estimating equations which define robustM-estimators. Application examples in the context of linear transformation models are considered. Monte Carlo studies are performed in order to assess the finite-sample performance of the inferential procedures based on quasi-and empirical likelihood, when the objective is the construction of robust confidence regions.

A note on the asymptotic behaviour of empirical likelihood statistics

This paper develops some theoretical results about the asymptotic behaviour of the empirical likelihood and the empirical profile likelihood statistics, which originate from fairly general estimating functions. The results accommodate, within a unified framework, various situations potentially occurring in a wide range of applications. For this reason, they are potentially useful in several contexts, such as, for example, in inference for dependent data. We provide examples showing that known findings in literature about the asymptotic behaviour of some empirical likelihood statistics in time series models can be derived as particular cases of our results.

On the Empirical Likelihood Ratio for Smooth Functions of M‐functionals

It is known that the empirical likelihood ratio can be used to construct confidence regions for smooth functions of the mean, Frechet differentiable statistical functionals and for a class of M-functionals. In this paper, we argue that this use can be extended to the class of functionals which are smooth functions of M-functionals. In particular, we find the conditions under which the empirical log-likelihood ratio for this kind of functionals admits a χ2 approxima tion. Furthermore, we investigate, by simulation methods, the related approximation error in some contexts of practical interest.

Simple Nonparametric Confidence Regions for the Evaluation of Continuous-Scale Diagnostic Tests

The evaluation of the ability of a diagnostic test to separate diseased subjects from non-diseased subjects is a crucial issue in modern medicine. The accuracy of a continuous-scale test at a chosen cut-off level can be measured by its sensitivity and specificity, i.e. by the probabilities that the test correctly identifies the diseased and non-diseased subjects, respectively.In practice, sensitivity and specificity of the test are unknown. Moreover, which cut-off level to use is also generally unknown in that no preliminary indications driving its choice could be available.In this paper, we address the problem of making joint inference on pairs of quantities defining accuracy of a diagnostic test, in particular, when one of the two quantities is the cut-off level. We propose a technique based on an empirical likelihood statistic that allows, within a unified framework, to build bivariate confidence regions for the pair (sensitivity, cut-off level) at a fixed value of specificity as well as for the pair (specificity, cut-off level) at a fixed value of sensitivity or the pair (sensitivity, specificity) at a fixed cut-off value.A simulation study is carried out to assess the finite-sample accuracy of the method. Moreover, we apply the method to two real examples.

Bias–corrected methods for estimating the receiver operating characteristic surface of continuous diagnostic tests

Verification bias is a well-known problem that may occur in the evaluation of predictive ability of diagnostic tests. When a binary disease status is considered, various solutions can be found in the literature to correct inference based on usual measures of test accuracy, such as the receiver operating characteristic (ROC) curve or the area underneath. Evaluation of the predictive ability of continuous diagnostic tests in the presence of verification bias for a three-class disease status is here discussed. In particular, several verification bias-corrected estimators of the ROC surface and of the volume underneath are proposed. Consistency and asymptotic normality of the proposed estimators are established and their finite sample behavior is investigated by means of Monte Carlo simulation studies. Two illustrations are also given.