Subventions et des contributions :

Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023)

Statistical inference with ranked data is inherently non-parametric. The strength of non-parametric statistics is that it can lead to efficient procedures while making few assumptions on the underlying distributions. On the other hand, non-parametric statistics does not generally rely on the use of a likelihood function, which limits the development of the usual inferential methods common in parametric statistics. Empirical likelihood methods have represented a major advance in this direction. Another advance consists of a parametric embedding of non-parametric inference problems to bridge the apparent gap between parametric and non-parametric statistics. My long term vision is two-fold: first, to integrate various non-parametric problems into the main stream of parametric statistics via a parametric embedding and second, to go beyond and make use of parametric methods in the embedded family to gain additional insight into various common non-parametric problems. The key to deriving fundamental results on non-parametric inference with the embedding approach lies in the appropriate choice of the parametric family. My short-term goals are to first revisit important developments in non-parametric and semi parametric inferences using this parametric embedding approach as a versatile tool that provides simplifying insights into complicated settings and extends optimality arguments from parametric to non-parametric and semi parametric problems. Then, I plan to build on some recent successes and further demonstrate that a likelihood function can be fruitfully defined for several non-parametric problems and to obtain new optimality results. The embedding approach is based on an adaptation of an earlier result of Neyman in which a smooth alternative distribution was defined for a goodness of fit problem. Combined with the use of the Rao score test, this leads to the asymptotic distribution of the score functions considered. In this way, it is possible for example, to obtain Friedman's test for randomized block design and to demonstrate its local optimality properties. In this proposal, I plan to extend the embedding approach to the more complicated setting involving left truncated and right censored (LTRC) data. As well, I plan to further exploit the use of penalized likelihood in order to reduce the dimension of the score functions considered. Another goal is to consider some real-world applications to relate this theory to practice. In terms of impact , this unified approach to non-parametric statistics is novel and is based on some of my recent results. It will provide additional tools for further development of methodology in various settings.
This proposal will train 8 HQP , who will develop skills in theoretical and practical statistical analysis of data, preparing them for careers as the case may be, in academia, government or private enterprise.