July 3rd 2015
Faculty of Economic and Business Sciences | Seminar 8
Una alternativa al p-AUC
2015/07/03 - 10:00 h | Alba Franco Pereira, Complutense University of Madrid
Acceptable specificities are high for early cancer detection tests. A lower specificity for a large population leads to many more falsely classified non-diseased subjects who may have to undergo a more invasive test subsequently. It is thus desired to compare screening markers at a higher range of specificities. The partial AUC, which summarizes part of the ROC curve in the range of desired specificities, use to be the alternative to AUC. The value of partial ROC analysis has been recognized and several methods have been developed. See McClish (1989), McClish (1990), Thompson and Zucchini (1989) and Obuchowski and McClish (1997). However, the methods for analysing partial ROC presented in these papers use a parametric approach which assumes the data have an underlying normal distribution. In this work we propose a new nonparametric partial summary measure, we evaluate its performance and compare it to the partial AUC.
Asymptotic distribution-free tests for semiparametric regressions
2015/07/03 - 10:40 h | Juan Carlos Pardo Fernández, University of Vigo
This article proposes a new general methodology for constructing nonparametric asymptotic distribution-free tests for semiparametric hypotheses in regression models. Tests are based on the difference between the estimated restricted and unrestricted regression errors' distributions. A suitable integral transformation of this difference renders the tests asymptotically distribution-free, with limits that are well-known functionals of a standard normal variable. Hence, the tests are straightforward to implement. The general methodology is illustrated with applications to testing for parametric models, semiparametric constrained mean-variance models and nonparametric significance. Several Monte Carlo studies show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes. (Joint work with Juan Carlos Escanciano and Ingrid Van Keilegom).
Fast goodness-of-fit tests based on the characteristic function
2015/07/03 - 11:40 h | María Dolores Jiménez Gamero, University of Sevilla
A class of goodness-of-fit tests for iid data whose test statistic is an L2 norm of the difference of the empirical characteristic function of the sample and a parametric estimate of the characteristic function in the null hypothesis, is considered. The null distribution is usually estimated through a parametric bootstrap. Although very easy to implement, the parametric bootstrap can become very computationally expensive as the sample size, the number of parameters or the dimension of the data increase. It is proposed to approximate the null distribution through a weighted bootstrap. The method is studied both theoretically and numerically. It provides a consistent estimator of the null distribution. In the numerical examples carried out, the estimated type I errors are close to the nominal values. The asymptotic properties are similar to those of the parametric bootstrap but, from a computational point of view, it is more efficient.
On nonparametric estimation of transition probabilities in non-Markov multi-state models
2015/07/03 - 12:20 h | Jacobo de Uña Álvarez, University of Vigo
Multi-state models are often used for modeling complex event history data. In these models the estimation of the transition probabilities is of particular interest, since they allow for long-term predictions of the process (Hougaard, 2000). Under random censoring, these quantities have been traditionally estimated by the Aalen-Johansen estimator (Aalen and Johansen, 1978), which is consistent if the process is Markov. However, for non-Markov processes, the Aalen-Johansen estimator will be in general biased. Several alternative estimators have been proposed in the recent literature (Meira-Machado et al., 2006; Allignol et al., 2014), and their superiority with respect to the Aalen-Johansen estimator has been proved in situations in which the Markov condition is strongly violated. However, such estimators have the drawback of requiring that the support of the censoring distribution contains the support of the lifetime distribution, which is not often the case. To overcome this issue, de Uña-Álvarez and Meira-Machado (2015) introduced a new nonparametric transition probability matrix which is a function of Kaplan-Meier estimators pertaining to several event times in certain subsamples. In this talk we revisit this estimator and we discuss some important practical issues, such as variance estimation, inclusion of covariates, and generalizations to more complicated forms of censoring and truncation. For illustration purposes, applications to real clinical data are given.