Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability-for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability—for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

Craniofacial characteristics of Caucasian and Afro-Caucasian Brazilian subjects with normal occlusion

OBJECTIVE: The objective of this study was to compare the skeletal, dental and soft tissue characteristics of Caucasian and Afro-Caucasian Brazilian subjects with normal occlusion and to evaluate sexual dimorphism within the groups. MATERIAL AND METHODS: The sample comprised lateral cephalograms of untreated normal occlusion subjects, divided into 2 groups. Group 1 included 40 Caucasian subjects (20 of each sex), with a mean age of 13.02 years; group 2 included 40 Afro-Caucasian subjects (20 of each sex), with a mean age of 13.02 years. Groups 1 and 2 and males and females within each group were compared with t tests. RESULTS: Afro-Caucasian subjects presented greater maxillary protrusion, smaller upper anterior face height and lower posterior face height, larger upper posterior face height, greater maxillary and mandibular dentoalveolar protrusion as well as soft tissue protrusion than Caucasian subjects. The Afro-Caucasian female subjects had less mandibular protrusion and smaller total posterior facial height and upper posterior facial height than males. CONCLUSIONS: Brazilian Afro-Caucasian subjects have greater dentoalveolar and soft tissue protrusion than Brazilian Caucasian subjects, with slight sexual dimorphism in some variables

The Skorokhod embedding problem and some families of Brownian martingales

Directeur de thèse : M. YorThèse Paris V

An explicit Skorokhod embedding for functionals of Markovian excursions

We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of Markovian excursions. Our setting allows to solve the Skorokhod embedding problem, in particular, for diffusions and their (signed, scaled) age processes, for Azema's martingale, for spectrally one-sided Levy processes and their reflected versions, for Bessel processes of dimension smaller than 2, and for their age processes, as well as for the age process of excursions of Cox-Ingersoll-Ross processes. This work is a continuation and an important generalization of Obloj and Yor (SPA 110). Our methodology is based on excursion theory and the solution to the Skorokhod embedding problem is described in terms of the Ito measure of the functional. We also derive an embedding for positive functionals and we correct a mistake in the formula for measures with atoms

An explicit solution to the Skorokhod embedding problem for functionals of excursions of Markov processes

We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of excursions of Markov processes. Our setting allows us to solve the Skorokhod embedding problem, in particular, for the age process of excursions of a Markov process, for diffusions and their signed age processes, for Azéma's martingale and for Bessel processes of dimension smaller than 2. This work is a continuation and an important generalization of Obłój and Yor [J. Obłój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83-110]. Our methodology is based on excursion theory and the solution to the Skorokhod embedding problem is described in terms of the Itô measure of the functional. We also derive an embedding for positive functionals and we correct a mistake in the formula of Obłój and Yor [J. Obłój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83-110] for measures with atoms. © 2006 Elsevier Ltd. All rights reserved

A complete characterization of local martingales which are functions of Brownian motion and its maximum

We prove the max-martingale conjecture given in recent article with Marc Yor. We show that for a continuous local martingale $(N\_t:t\ge 0)$ and a function $H:R x R\_+\to R$, $H(N\_t,\sup\_{s\leq t}N\_s)$ is a local martingale if and only if there exists a locally integrable function $f$ such that $H(x,y)=\int\_0^y f(s)ds-f(y)(x-y)+H(0,0)$. This implies readily, via Levy's equivalence theorem, an analogous result with the maximum process replaced by the local time at 0

Robust estimation of superhedging prices

We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plug-in estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this, we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale densities. We then extend our study, in part, to estimation of risk measures, to the case of markets with traded options, to a multi-period setting and to settings with model uncertainty. We also study convergence rates of estimators and convergence of super-hedging strategies

An explicit Skorokhod embedding for the age of Brownian excursions and Azema martingale

A general methodology allowing to solve the Skorokhod stopping problem for positive functionals of Brownian excursions, with the help of Brownian local time, is developed. The stopping times we consider have the following form: Tμ=inf{t>0: Ft≥μF(Lt)}. As an application, the Skorokhod embedding problem for a number of functionals (Ft: t≥0), including the age (length) and the maximum (height) of excursions, is solved. Explicit formulae for the corresponding stopping times Tμ, such that FTμ∼μ, are given. It is shown that the function μF is the same for the maximum and for the age, μ=ψ μ-1, where ψμ(x) =∫[0,x](y/μ̄(y)) dμ(y). The joint law of (gTμ,Tμ, LTμ), in the case of the age functional, is characterized. Examples for specific measures μ are discussed. Finally, a randomized solution to the embedding problem for Azéma martingale is deduced. Throughout the article, two possible approaches, using excursions and martingale theories, are presented in parallel. © 2003 Elsevier B.V. All rights reserved