Contributions to inference for diffusion processes and robust statistics

Diplôme Thèse Contributions to inference for diffusion processes and robust statistics eng 2017-10-24 author Deleamont Pierre-Yves 811708 director Ronchetti Elvezio 0000-0003-2231-4556 22756 director La Vecchia Davide 0000-0001-7572-268X 844164 10.13097/archive-ouverte/unige:99923 urn:nbn:ch:unige-999235 GSEM 46 This thesis is composed of two parts. The first part is devoted to inference for discretely observed diffusion processes. We first describe the general methodology of martingale estimating functions and show that this technique is particularly well suited to polynomial diffusions. We then use that theory as a building block to devise a new class of estimators for locally stationary diffusions. The second part of the thesis is concerned with problems related to robustness theory. We derive robust estimators and tests for randomly censored survival data, which arise when the time until a certain event occurs is not fully observable. Then, we study the general convex loss Lasso for the linear model in a high-dimensional setting. We present new bounds for the estimation and prediction errors, and show how these bounds depend on the choice of the loss function through a well-known term in robust statistics. Diffusion processes martingale estimating functions local stationarity robust statistics censored data Dewey 310 117 Research Center for Statistics S5 false c31235e7-0e86-47c5-818a-4000a8f1b6a4 Thesis Restricted Thesis_Deleamont.pdf 2532626 application/pdf 696533e6fc1ce58b66cb0bd19ed13c7ef69cc63bd804c3aa98bcaaa0aad5f00b restrictedAccess Faculté d'économie et de management / Research Center for Statistics

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Contributions to inference for diffusion processes and robust statistics				2017	855	34

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Deleamont, Pierre-Yves