June 19th 2014
Faculty of Economic and Business Sciences | Salón de Grados
Generalized copula-graphic estimation with left-truncated and right-censored data
2014/06/19 – 12:15 h | Jacobo de Uña Álvarez, University of Vigo
Abstract
In this paper a copula-graphic estimator is proposed for left-truncated and right-censored survival data. It is assumed that there is some dependent censoring acting on the variable of interest, which may come from an existing competing risk. Furthermore, the full process is independently right-censored by some administrative censoring time, while there is an independent left-truncation variable which complicates the sampling procedure. The dependent censoring is modeled through an Archimedean copula function, which is supposed to be known. An asymptotic representation of the estimator as a sum of independent and identically distributed random variables is obtained and, consequently, a central limit theorem is established. These results extend to the truncated setting those in de Uña-Álvarez and Veraverbeke (2013). We investigate the finite sample performance of the estimator through simulations. A real data illustration is included. This is joint work with Noël Veraverbeke.
Mode testing for circular data
2014/06/19 – 13:00 h | Alberto Rodríguez Casal, University of Santiago de Compostela
Abstract
Probability density functions fully describe the behavior of random variables, although in many cases, a complete characterization is not necessary and the main interest is to determine which variable values are most likely. For continuous random variables, this procedure is just the identification of the density modes (local maxima of the probability density function). There are several alternatives for detecting modes in scalar variables. Although there are various exploratory tools, like the SiZer method proposed by 1, these do not provide a formal statistical hypothesis test. Within this context, it is worth mentioning the critical bandwidth, see 2, and also those tests based on the excess mass, see 3. In this work, we propose a new procedure for calibrating the excess mass statistics based on the critical bandwidth. This idea is also adapted to the circular data context. The behavior of the proposed tests is analyzed thought a extensive simulation study. Finally, the methodology is used to study the seasonal patterns of forest fires in different geographic regions.
References:
1 Chaudhuri, P. and Marron, J. S. (1999). SiZer for Exploration of Structures in Curves. Journal of the American Statistical Association 94, 807–823.
2 Hall, P. and York, M. (2001). On the calibration of Silverman’s test for multimodality. Statistica Sinica 11, 515–536.
3 Müller, D.W. and Sawitzki, G. (1991). Excess Mass Estimates and Tests for Multimodality. Journal of the American Statistical Association, 86, 738–746.