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Houdré,
Christian
Houdré,
Christian
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12 results
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ItemGraduate student conference on probability(Georgia Institute of Technology, 2013-04-01) Houdré, Christian
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ItemTopics in sequence comparison and discrete structures(Georgia Institute of Technology, 2011-05-11) Houdré, Christian ; Matzinger, Heinrich
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ItemConverse Poincaré Type Inequalities for Convex Functions(Georgia Institute of Technology, 2009-12-07) Bobkov, S. G. ; Houdré, ChristianConverse Poincaré type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.
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ItemNonparametric estimation for Levy processes with a view towards mathematical finance(Georgia Institute of Technology, 2004-11) Figueroa-Lopez, Enrique ; Houdré, ChristianNonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be written in terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A model selection approach made up of two steps is investigated. The first step consists in the selection of a good estimator from a linear model of proposed Levy densities, while the second is a data-driven selection of a linear model among a given collection of linear models. By providing lower bounds for the minimax risk of estimation over Besov Levy densities, our estimators are shown to achieve the "best" rate of convergence. A numerical study for the case of histogram estimators and for variance Gamma processes, models of key importance in risky asset price modeling driven by Levy processes, is presented.
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ItemExponential Inequalities for U-Statistics of Order Two with Constants(Georgia Institute of Technology, 2002-12-13) Houdré, Christian ; Reynaud-Bouret, Patricia
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ItemSharp Constants in Some Multiplicative Sobolev Inequalities(Georgia Institute of Technology, 1995-09-16) Bobkov, S. G. ; Houdré, ChristianThe optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1-norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities turn out to still be equivalent to the isoperimetric property of the balls in the Euclidean space. In the course of the proof, relations between Lorentz and Lebesgue spaces are studied (and also applied to some different measures, e.g., Riesz potentials).
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ItemOn the Linear Prediction of Some L^p Random Fields(Georgia Institute of Technology, 1995-08) Cheng, R. ; Houdré, ChristianThis work is concerned with the prediction problem for a class of L^p-random fields. For this class of fields, we derive prediction error formulas, spectral factorizations, and orthogonal decompositions.
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ItemA Characterization of Gaussian Measures via the Isoperimetric Property of Half-Spaces(Georgia Institute of Technology, 1995-07-25) Bobkov, S. G. ; Houdré, ChristianIf the half-spaces of the form {x\in R^n: x_1 \le c} are extremal in the isoperimetric problem for the product measure \mu^n, n\ge 2, then \mu is Gaussian.
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ItemIsoperimetric Constants for Product Probability Measures(Georgia Institute of Technology, 1995-07-24) Bobkov, S. G. ; Houdré, ChristianA dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived.
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ItemDimension Free Weak Concentration of Measure Phenomenon(Georgia Institute of Technology, 1995-07-24) Bobkov, S. G. ; Houdré, ChristianFor product probability measures \mu^n, we obtain necessary and sufficient conditions (in terms of \mu) for dimension free isoperimetric inequalities of the form \mu^n (A + h[-1,1]^n)\ge R_h(\mu^n(A)) to hold; for a function R such that R(p) > p, for all (some) p \in (0,1), and for h > 0 large enough. Some questions related to the concentration of measure phenomenon are also discussed.