14:30 Marc Hallin, ECARES, ULB
From distribution-freeness to semiparametric efficiency : sixty years of rank-based inference
Abstract: The modern history of ranks in statistics started in 1945 with Frank Wilcoxon's pathbreaking three pages on rank tests for location. Emphasis in 1945 was on distribution-freeness and ease of application. Since then, under the impulse of such names as Chernoff, Savage, Hodges, Lehmann, Hajek, and Le Cam, rank-based methods have followed the development of contemporary statistics, and turned into a complete body of modern, flexible and powerful techniques. In this talk, we show how this evolution, from distribution-freeness to group invariance and tangent space projections, eventually may reconcile the enemy brothers of statistics efficiency and robustness.
16:00 Ingrid Van keilegom, Institut de Statistique, UCL
Semiparametric modeling and estimation of the dispersion function in regression
Abstract: Modeling heteroscedasticity in semiparametric regression can improve the efficiency of the estimator of the parametric component in the regression function, and is important for inference problems such as plug-in bandwidth selection and the construction of confidence intervals. However, the literature on exploring heteroscedasticity in a semiparametric setting is rather limited. Existing work is mostly restricted to the partially linear mean regression model with a fully nonparametric variance structure. The nonparametric modeling of heteroscedasticity is hampered by the curse of dimensionality in practice. Moreover, the approaches used in existing work need to assume smooth objective functions, therefore exclude the emerging important class of semiparametric quantile regression models. To overcome these drawbacks, we propose a general semiparametric location-dispersion regression framework, which enriches the currently available semiparametric regression models. With our general framework, we do not need to impose a special semiparametric form for the location or dispersion function. Rather, we provide easy to check sufficient conditions such that the asymptotic normality theory we establish is valid for many commonly used semiparametric structures, for instance, the partially linear structure and singleindex structure. Our theory permits non-smooth location or dispersion functions, thus allows for semiparametric quantile heteroscedastic regression. We demonstrate the proposed method via simulations and the analysis of a real data set. (This is joint work with Lan Wang).