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The Gamma Stein equation and non-central de Jong theorems Döbler, Christian ; Peccati, Giovanni in Bernoulli (in press) Detailed reference viewed: 253 (15 UL)Limit theorems for integral functionals of Hermite-driven processes Garino, Valentin ; Nourdin, Ivan ; et al in Bernoulli (2021), 27(3), 1764-1788 Detailed reference viewed: 112 (19 UL)Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces Thompson, James ; Thalmaier, Anton in Bernoulli (2020), 26(3), 2202-2225 In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian ... [more ▼] In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian geometry. Firstly, we consider sub-Riemannian limits of Riemannian foliations. Secondly, we consider the non-smooth setting of RCD*(K,N) spaces. In each case the necessary ingredients are an Ito formula and a comparison theorem for the Laplacian, for which we refer to the recent literature. As an application, we derive pointwise Carmona-type estimates on eigenfunctions of Schrodinger operators. [less ▲] Detailed reference viewed: 214 (45 UL)Estimation of the linear fractional stable motion ; ; Podolskij, Mark in Bernoulli (2020), 26(1), 226252 Detailed reference viewed: 103 (2 UL)Maximum likelihood characterization of distributions ; ; Swan, Yvik 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 ▲] Detailed reference viewed: 107 (1 UL)Universal Gaussian fluctuations on the discrete Poisson chaos Peccati, Giovanni ; in Bernoulli (2014), 20(2), 697-715 Detailed reference viewed: 121 (0 UL)Invariance principles for homogeneous sums of free random variables ; Nourdin, Ivan in Bernoulli (2014), 20(2), 586-603 Detailed reference viewed: 122 (1 UL)Probabilistic aspects of finance Föllmer, Hans ; in Bernoulli (2013), 19(4), 1306-1326 Detailed reference viewed: 107 (2 UL)Group representations and high-resolution central limit theorems for subordinated spherical random fields ; Peccati, Giovanni in Bernoulli (2010), 16(3), 798--824 Detailed reference viewed: 156 (0 UL)Limit theorems for nonlinear functionals of Volterra processes via white noise analysis ; Nourdin, Ivan ; in Bernoulli (2010), 16(4), 1262-1293 Detailed reference viewed: 120 (2 UL)A Bernstein-type inequality for suprema of random processes with applications to model selection in non-Gaussian regression Baraud, Yannick in Bernoulli (2010), 16(4), 1064--1085 Detailed reference viewed: 137 (8 UL)Multiple integral representation for functionals of Dirichlet processes Peccati, Giovanni in Bernoulli (2008), 14(1), 91--124 Detailed reference viewed: 150 (0 UL)Central limit theorems for double Poisson integrals Peccati, Giovanni ; in Bernoulli (2008), 14(3), 791--821 Detailed reference viewed: 139 (0 UL)Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2 ; Nourdin, Ivan in Bernoulli (2008), 14(3), 822-837 Detailed reference viewed: 47 (1 UL)Multivariate Wavelet-Based Shape Preserving Estimation for Dependent Observations Cosma, Antonio ; ; 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 ▲] Detailed reference viewed: 112 (8 UL)Correcting Newton-Cotes integrals by Lévy areas Nourdin, Ivan ; in Bernoulli (2007), 13(3), 695-711 Detailed reference viewed: 105 (2 UL)Explicit formulae for time-space Brownian chaos Peccati, Giovanni in Bernoulli (2003), 9(1), 25--48 Detailed reference viewed: 130 (0 UL)Non-asymptotic minimax rates of testing in signal detection Baraud, Yannick in Bernoulli (2002), 8(5), 577--606 Detailed reference viewed: 60 (4 UL) |
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