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Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…

Econometrics · Economics 2026-03-20 Claudia Noack , Tomasz Olma , Christoph Rothe

Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…

Methodology · Statistics 2019-05-13 Espen Bernton , Pierre E. Jacob , Mathieu Gerber , Christian P. Robert

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Statistics Theory · Mathematics 2024-02-14 Aryeh Kontorovich , Amichai Painsky

We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…

Mathematical Physics · Physics 2024-07-19 Gaëtan Borot , Alice Guionnet

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows…

Probability · Mathematics 2023-04-07 Denis Belomestny , Pierre Menard , Alexey Naumov , Daniil Tiapkin , Michal Valko

This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained proofs. Our results are sharp and minimizers are obtained in…

Analysis of PDEs · Mathematics 2021-12-01 Cristian Cazacu , Joshua Flynn , Nguyen Lam

The classical Gaussian concentration inequality for Lipschitz functions is adapted to a setting where the classical assumptions (i.e. Lipschitz and Gaussian) are not met. The theory is more direct than much of the existing theory designed…

Probability · Mathematics 2022-05-16 Daniel J. Fresen

In this paper we introduce the perturbed version of the Barab\'asi-Albert random graph with multiple type edges and prove the existence of the (generalized) asymptotic degree distribution. Similarly to the non-perturbed case, the asymptotic…

Probability · Mathematics 2019-09-19 Ágnes Backhausz , Bence Rozner

We prove two estimates for the Barban--Davenport--Halberstam type variance of a general complex sequence in arithmetic progressions. The proofs are elementary, and our estimates are capable of yielding an asymptotic for the variance when…

Number Theory · Mathematics 2024-12-30 Adam J. Harper

In this note, we study the convergence from the discrete to the continuous non-linear Fourier transform. Relations between spectral problems and questions in complex function theory provide a new approach to the study of scattering problems…

Classical Analysis and ODEs · Mathematics 2024-08-16 Ashley R. Zhang

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…

Statistics Theory · Mathematics 2021-04-23 Graeme Auld , Ioannis Papastathopoulos

This German paper discusses certain aspects of the non-degenerate case of truncated matricial moment problems on the intervals [$\alpha$,$\infty$) and (-$\infty$,\alpha] for any real number $\alpha$.

Classical Analysis and ODEs · Mathematics 2017-03-21 Benjamin Jeschke

In this paper, we provide estimates for the additive discretized energy of \[\sum_{c\in C} |\{(a_1, a_2, b_1, b_2)\in A^2\times B^2: |(a_1 +cb_1) - (a_2 + cb_2)|\le \delta\}|_{\delta},\] that depend on non-concentration conditions of the…

Classical Analysis and ODEs · Mathematics 2024-03-29 Quy Pham , Thang Pham , Chun-Yen Shen

In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete. By using Contraction Mapping Theorem, we establish conditions under…

Classical Analysis and ODEs · Mathematics 2018-03-09 Raziye Mert , Allan Peterson , Thabet Abdeljawad , Lynn Erbe

We derive the non-asymptotical non-uniform sharp error estimation for Bernstein's approximation of continuous function based on the modern probabilistic apparatus. We investigate also the convergence of derivative of these polynomials and…

Functional Analysis · Mathematics 2015-08-31 Eugene Ostrovsky , Leonid Sirota

Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit…

Methodology · Statistics 2025-06-24 Sally Paganin , Garritt L. Page , Fernando Andrés Quintana

Linear mixed effects are considered excellent predictors of cluster-level parameters in various domains. However, previous work has shown that their performance can be seriously affected by departures from modelling assumptions. Since the…

Methodology · Statistics 2022-07-27 Katarzyna Reluga , Stefan Sperlich

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…

Quantitative Methods · Quantitative Biology 2009-11-11 Noam Slonim , Gurinder Singh Atwal , Gasper Tkacik , William Bialek

We consider the problem of inference after model selection under weak assumptions in the time series setting. Even when the data are not independent, we show that sample splitting remains asymptotically valid as long as the process…

Statistics Theory · Mathematics 2019-02-27 Robert Lunde

This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain…

Numerical Analysis · Computer Science 2018-05-16 Svetlana Matculevich , Monika Wolfmayr