The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Judith Rousseau - One of the best experts on this subject based on the ideXlab platform.
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Bernstein Von Mises Theorem for Linear Functionals of the density
Annals of Statistics, 2012Co-Authors: Vincent Rivoirard, Judith RousseauAbstract:In this paper, we study the asymptotic posterior distribution of Linear Functionals of the density by deriving general conditions to obtain a semi-parametric version of the Bernstein-von Mises theorem. The special case of the cumulative distributive function evaluated at a specific point is widely considered. In particular, we show that for infinite dimensional exponential families, under quite general assumptions, the asymptotic posterior distribution of the functional can be either Gaussian or a mixture of Gaussian distributions with different centering points. This illustrates the positive but also the negative phenomena that can occur for the study of Bernstein-von Mises results.
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bernstein von mises theorem for Linear Functionals of the density
arXiv: Statistics Theory, 2009Co-Authors: Vincent Rivoirard, Judith RousseauAbstract:In this paper, we study the asymptotic posterior distribution of Linear Functionals of the density. In particular, we give general conditions to obtain a semiparametric version of the Bernstein-Von Mises theorem. We then apply this general result to nonparametric priors based on infinite dimensional exponential families. As a byproduct, we also derive adaptive nonparametric rates of concentration of the posterior distributions under these families of priors on the class of Sobolev and Besov spaces.
Francisco Marcellan - One of the best experts on this subject based on the ideXlab platform.
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Geronimus transformations of bivariate Linear Functionals
Journal of Mathematical Analysis and Applications, 2020Co-Authors: Francisco Marcellan, Misael E. Marriaga, Teresa E. Pérez, Miguel A. PiñarAbstract:Abstract Given a Linear functional u in the Linear space of polynomials in two variables with real coefficients and a polynomial λ ( x , y ) , in this contribution we deal with Geronimus transformations of u, i.e., those Linear Functionals v such that u = λ ( x , y ) v . The connection formulas between the sequences of bivariate orthogonal polynomials with respect to u and v are given. A matrix interpretation of such transformations by using LU and UL factorizations of the block Jacobi matrices associated with such polynomials is given. Finally, some illustrative examples of Geronimus transformations of weight function supported in domains of R 2 are discussed.
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Semi-classical Linear Functionals of class three: the symmetric case
Journal of Difference Equations and Applications, 2013Co-Authors: Francisco Marcellan, M. Sghaier, M. ZaatraAbstract:In this paper, we obtain all the symmetric semi-classical Linear Functionals of class three taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention on their integral representations. Thus, some Linear Functionals very well known in the literature, associated with perturbations of semi-classical Linear Functionals of class one at most, appear as well as new Linear Functionals which have not been studied.
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On semiclassical Linear Functionals of class s=2: classification and integral representations
Journal of Difference Equations and Applications, 2012Co-Authors: Francisco Marcellan, M. Sghaier, M. ZaatraAbstract:In this paper, we obtain all the semiclassical Linear Functionals of class two taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention in their integral representations. Thus, some Linear Functionals very well known in the literature, associated with perturbations of classical Linear Functionals, as well as new Linear Functionals appear which have not been studied as far as we know.
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Christoffel Transforms and Hermitian Linear Functionals
Mediterranean Journal of Mathematics, 2005Co-Authors: Francisco Marcellan, Javier HernándezAbstract:In this contribution we are focused on some spectral transformations of Hermitian Linear Functionals. They are the analogues of the Christoffel transform for Linear Functionals, i. e. for Jacobi matrices which has been deeply studied in the past. We consider Hermitian Linear Functionals associated with a probability measure supported on the unit circle. In such a case we compare the Hessenberg matrices associated with such a probability measure and its Christoffel transform. In this way, almost unitary matrices appear. We obtain the deviation to the unit matrix both for principal submatrices and the complete matrices respectively.
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Perturbations of Laguerre-Hahn Linear Functionals
Journal of Computational and Applied Mathematics, 1999Co-Authors: Francisco Marcellan, E. PrianesAbstract:Abstract In this paper we shall make some perturbations in a Laguerre–Hahn Linear functional, such as the addition of a Dirac Delta or the left multiplication by a polynomial. We shall study that these transformations carried out on Laguerre–Hahn Linear Functionals originate new Laguerre–Hahn Linear Functionals. We shall also analyze the class of the resulting functional.
Vincent Rivoirard - One of the best experts on this subject based on the ideXlab platform.
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Bernstein Von Mises Theorem for Linear Functionals of the density
Annals of Statistics, 2012Co-Authors: Vincent Rivoirard, Judith RousseauAbstract:In this paper, we study the asymptotic posterior distribution of Linear Functionals of the density by deriving general conditions to obtain a semi-parametric version of the Bernstein-von Mises theorem. The special case of the cumulative distributive function evaluated at a specific point is widely considered. In particular, we show that for infinite dimensional exponential families, under quite general assumptions, the asymptotic posterior distribution of the functional can be either Gaussian or a mixture of Gaussian distributions with different centering points. This illustrates the positive but also the negative phenomena that can occur for the study of Bernstein-von Mises results.
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bernstein von mises theorem for Linear Functionals of the density
arXiv: Statistics Theory, 2009Co-Authors: Vincent Rivoirard, Judith RousseauAbstract:In this paper, we study the asymptotic posterior distribution of Linear Functionals of the density. In particular, we give general conditions to obtain a semiparametric version of the Bernstein-Von Mises theorem. We then apply this general result to nonparametric priors based on infinite dimensional exponential families. As a byproduct, we also derive adaptive nonparametric rates of concentration of the posterior distributions under these families of priors on the class of Sobolev and Besov spaces.
M. Zaatra - One of the best experts on this subject based on the ideXlab platform.
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Semi-classical Linear Functionals of class three: the symmetric case
Journal of Difference Equations and Applications, 2013Co-Authors: Francisco Marcellan, M. Sghaier, M. ZaatraAbstract:In this paper, we obtain all the symmetric semi-classical Linear Functionals of class three taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention on their integral representations. Thus, some Linear Functionals very well known in the literature, associated with perturbations of semi-classical Linear Functionals of class one at most, appear as well as new Linear Functionals which have not been studied.
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On semiclassical Linear Functionals of class s=2: classification and integral representations
Journal of Difference Equations and Applications, 2012Co-Authors: Francisco Marcellan, M. Sghaier, M. ZaatraAbstract:In this paper, we obtain all the semiclassical Linear Functionals of class two taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention in their integral representations. Thus, some Linear Functionals very well known in the literature, associated with perturbations of classical Linear Functionals, as well as new Linear Functionals appear which have not been studied as far as we know.
Christoph Thale - One of the best experts on this subject based on the ideXlab platform.
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new berry esseen bounds for non Linear Functionals of poisson random measures
Electronic Journal of Probability, 2014Co-Authors: Peter Eichelsbacher, Christoph ThaleAbstract:This paper deals with the quantitative normal approximation of non-Linear Functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein's method with the Malliavin calculus of variations on the Poisson space, we derive a bound, which is strictly smaller than what is available in the literature. This is applied to sequences of multiple integrals and sequences of Poisson Functionals having a finite chaotic expansion. This leads to new Berry-Esseen bounds in a Poissonized version of de Jong's theorem for degenerate U-statistics. Moreover, geometric Functionals of intersection processes of Poisson $k$-flats, random graph statistics of the Boolean model and non-Linear Functionals of Ornstein-Uhlenbeck-Levy processes are considered.
