References of "Bernoulli"
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See detailThe Gamma Stein equation and non-central de Jong theorems
Döbler, Christian UL; Peccati, Giovanni UL

in Bernoulli (in press)

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See detailUniversal Gaussian fluctuations on the discrete Poisson chaos
Peccati, Giovanni UL; Zheng, Cengbo

in Bernoulli (2014), 20(2), 697-715

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See detailInvariance principles for homogeneous sums of free random variables
Deya, Aurélien; Nourdin, Ivan UL

in Bernoulli (2014), 20(2), 586-603

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See detailMaximum likelihood characterization of distributions
Duerinckx, Mitia; Ley, Christophe; Swan, Yvik UL

in Bernoulli (2014), 20(2), 775-802

A famous characterization theorem due to C. F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and ... [more ▼]

A famous characterization theorem due to C. F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There exist many extensions of this result in diverse directions, most of them focussing on location and scale families. In this paper we propose a unified treatment of this literature by providing general MLE characterization theorems for one-parameter group families (with particular attention on location and scale parameters). In doing so we provide tools for determining whether or not a given such family is MLE-characterizable, and, in case it is, we define the fundamental concept of minimal necessary sample size at which a given characterization holds. Many of the cornerstone references on this topic are retrieved and discussed in the light of our findings, and several new characterization theorems are provided. Of particular interest is that one part of our work, namely the introduction of so-called equivalence classes for MLE characterizations, is a modernized version of Daniel Bernoulli's viewpoint on maximum likelihood estimation. [less ▲]

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See detailProbabilistic aspects of finance
Föllmer, Hans UL; Schied, Alexander

in Bernoulli (2013), 19(4), 1306-1326

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See detailGroup representations and high-resolution central limit theorems for subordinated spherical random fields
Marinucci, Domenico; Peccati, Giovanni UL

in Bernoulli (2010), 16(3), 798--824

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See detailLimit theorems for nonlinear functionals of Volterra processes via white noise analysis
Darses, Sébastien; Nourdin, Ivan UL; Nualart, David

in Bernoulli (2010), 16(4), 1262-1293

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See detailCentral limit theorems for double Poisson integrals
Peccati, Giovanni UL; Taqqu, Murad S.

in Bernoulli (2008), 14(3), 791--821

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See detailAsymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2
Darses, Sébastien; Nourdin, Ivan UL

in Bernoulli (2008), 14(3), 822-837

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See detailMultiple integral representation for functionals of Dirichlet processes
Peccati, Giovanni UL

in Bernoulli (2008), 14(1), 91--124

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See detailCorrecting Newton-Cotes integrals by Lévy areas
Nourdin, Ivan UL; Simon, Thomas

in Bernoulli (2007), 13(3), 695-711

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See detailMultivariate Wavelet-Based Shape Preserving Estimation for Dependent Observations
Cosma, Antonio UL; Scaillet, Olivier; Von Sachs, Rainer

in Bernoulli (2007), 13(2), 301-329

We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape ... [more ▼]

We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. As important application, we discuss conditional quantile estimation for financial time series data. We show that our methodology can be easily implemented with B-splines, and performs well in a finite sample situation, through Monte Carlo simulations. [less ▲]

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See detailExplicit formulae for time-space Brownian chaos
Peccati, Giovanni UL

in Bernoulli (2003), 9(1), 25--48

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See detailNon-asymptotic minimax rates of testing in signal detection
Baraud, Yannick UL

in Bernoulli (2002), 8(5), 577--606

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