Intervalli di confidenza non parametrici per l'area sottesa alla curva ROC.

Seguendo un\u2019idea di Jing et al. (2005), in questo lavoro si combinano la funzione di verosimiglianza empirica per il funzionale media e gli pseudo-valori jackknife derivati dalla statistica di Mann-Whitney per due campioni. Ci\uf2 permette di ottenere una funzione di pseudo-verosimiglianza L(\u3c1) per l\u2019area \u3c10 sottesa alla curva ROC. Si dimostra che vale un risultato asintotico analogo al teorema di Wilks, cosicch\ue9 L(\u3c1) pu\uf2 essere usata, nella maniera usuale, per ottenere intervalli di confidenza approssimati per \u3c10. Vengono inoltre forniti alcuni risultati di simulazione che mostrano l\u2019utilit\ue0 del metodo proposto

Semiparametric interval estimation of Pr[Y > X]

Let X and Y be two independent continuous random variables. We discuss three techniques to obtain confidence intervals for ρ_Pr[Y > X] in a semiparametric framework. One method relies on the asymptotic normality of an estimator for ρ; 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 dataset on the detection of carriers of Duchenne Muscular Dystrophy

Quasi-profile loglikelihoods 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 to the corresponding quasi-profile score function to have bias and information bias of order 0(1). We illustrate the use of the proposed pseudo-likelihood with an application for robust inference in linear models

Second-order accurate confidence regions based on members of the generalised power divergence family

Recently, a technique based on pseudo-observations has been proposed to tackle the so called convex hull problem for the empirical likelihood statistic. The resulting adjusted empirical likelihood also achieves the highorder precision of the Bartlett correction. Nevertheless, the technique induces an upper bound on the resulting statistic that may lead, in certain circumstances, to worthless confidence regions equal to the whole parameter space. In this paper we show that suitable pseudo-observations can be deployed to make each element of the generalised power divergence family Bartlett-correctable and released from the convex hull problem. Our approach is conceived to achieve this goal by means of two distinct sets of pseudo-observations with dfferent tasks. An important effect of our formulation is to provide a solution that permits to overcome the problem of the upper bound. The proposal, whose effectiveness is confirmed by simulation results, gives back attractiveness to a broad class of statistics that potentially contains good alternatives to the empirical likelihood

Nearest-neighbor estimation for ROC analysis under verification bias

For a continuous-scale diagnostic test, the receiver operating characteristic (ROC) curve is a popular tool for displaying the ability of the test to discriminate between healthy and diseased subjects. In some studies, verification of the true disease status is performed only for a subset of subjects, possibly depending on the test result and other characteristics of the subjects. Estimators of the ROC curve based only on this subset of subjects are typically biased; this is known as verification bias. Methods have been proposed to correct verification bias, in particular under the assumption that the true disease status, if missing, is missing at random (MAR). MAR assumption means that the probability of missingness depends on the true disease status only through the test result and observed covariate information. However, the existing methods require parametric models for the (conditional) probability of disease and/or the (conditional) probability of verification, and hence are subject to model misspecification: a wrong specification of such parametric models can affect the behavior of the estimators, which can be inconsistent. To avoid misspecification problems, in this paper we propose a fully nonparametric method for the estimation of the ROC curve of a continuous test under verification bias. The method is based on nearest-neighbor imputation and adopts generic smooth regression models for both the probability that a subject is diseased and the probability that it is verified. Simulation experiments and an illustrative example show the usefulness of the new method. Variance estimation is also discussed

Nonparametric estimation of ROC surfaces under verification bias: supplementary material.

none3noSupplementary Material for paper: Nonparametric estimation of ROC surfaces under verification bias published on REVSTAT STATISTICAL JOURNAL, 2020, 18, 697 - 720noneTO, DUC KHANH; Chiogna Monica; Adimari GianfrancoTO, DUC KHANH; Chiogna Monica; Adimari Gianfranc