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This work resolves the following question in non-Euclidean statistics: Is it possible to consistently estimate the Fr\'echet mean set of an unknown population distribution, with respect to the Hausdorff metric, when given access to…

Statistics Theory · Mathematics 2025-07-02 Moise Blanchard , Adam Quinn Jaffe

We propose elliptical graphical models based on conditional uncorrelatedness as a general- ization of Gaussian graphical models by letting the population distribution be elliptical instead of normal, allowing the fitting of data with…

Methodology · Statistics 2015-06-16 Daniel Vogel , Roland Fried

In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient…

Optimization and Control · Mathematics 2023-07-03 Akash Mondal , Prashanth L. A. , Shalabh Bhatnagar

Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for…

Statistics Theory · Mathematics 2007-09-14 Bert van Es , Shota Gugushvili , Peter Spreij

It was shown in Groeneboom (1983) that the least concave majorant of one-sided Brownian motion without drift can be characterized by a jump process with independent increments, which is the inverse of the process of slopes of the least…

Probability · Mathematics 2013-03-26 Piet Groeneboom

The problem of determining a periodic Lipschitz vector field $b=(b_1, \dots, b_d)$ from an observed trajectory of the solution $(X_t: 0 \le t \le T)$ of the multi-dimensional stochastic differential equation \begin{equation*} dX_t =…

Statistics Theory · Mathematics 2020-07-21 Richard Nickl , Kolyan Ray

The center of gravity is one of the most frequently used algorithm for position reconstruction with different analytical forms for the noise optimization. The error distributions of the different forms are essential instruments to improve…

Instrumentation and Detectors · Physics 2020-12-01 Gregorio Landi , Giovanni E. Landi

This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the limiting extreme order statistics: a branching…

Probability · Mathematics 2021-07-13 Jim Pitman , Wenpin Tang

We prove a connection between the Green's function of the fractional Anderson model and the two point function of a self-avoiding random walk with long range jumps, adapting a strategy proposed by Schenker in 2015. This connection allows us…

Mathematical Physics · Physics 2024-03-05 Margherita Disertori , Roberto Maturana Escobar , Constanza Rojas-Molina

We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at…

Statistical Mechanics · Physics 2024-07-02 Federico Gerbino , Pierre Le Doussal , Guido Giachetti , Andrea De Luca

We consider compact Grassmann manifolds $G/K$ over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type $BC$. From an explicit integral representation of these polynomials we deduce a…

Classical Analysis and ODEs · Mathematics 2015-02-11 Margit Rösler , Michael Voit

This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…

Statistics Theory · Mathematics 2009-08-21 Liqun Wang

This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN({\alpha}, r, {\mu}, {\sigma}^2 ) that result from summing independent gamma({\alpha}, r) and N({\mu}, {\sigma}^2 ) random…

Applications · Statistics 2024-12-03 Massimiliano Bonamente , Dale Zimmerman

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…

Econometrics · Economics 2024-02-27 Felix Chan , Laszlo Matyas

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the…

Chaotic Dynamics · Physics 2009-10-31 E. Bogomolny , U. Gerland , C. Schmit

A Chernoff-type distribution is a nonnormal distribution defined by the slope at zero of the greatest convex minorant of a two-sided Brownian motion with a polynomial drift. While a Chernoff-type distribution is known to appear as the…

Statistics Theory · Mathematics 2021-06-23 Qiyang Han , Kengo Kato

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…

Statistics Theory · Mathematics 2019-07-09 Ankit Pensia , Varun Jog , Po-Ling Loh

It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…

Information Theory · Computer Science 2026-05-26 Leighton P. Barnes , Alex Dytso

We provide a uniform framework to compute the exact distribution of the number of minima/maxima in three different random walk landscape models in one dimension. The landscape is generated by the trajectory of a discrete-time continuous…

Statistical Mechanics · Physics 2025-08-04 Anupam Kundu , Satya N. Majumdar , Gregory Schehr