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This paper studies inference in randomized controlled trials with covariate-adaptive randomization when there are multiple treatments. More specifically, we study inference about the average effect of one or more treatments relative to…

Econometrics · Economics 2019-01-21 Federico A. Bugni , Ivan A. Canay , Azeem M. Shaikh

We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…

Statistics Theory · Mathematics 2022-11-01 Akira Shinkyu

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…

Statistics Theory · Mathematics 2026-02-10 Jiming Jiang , Matt P. Wand , Swarnadip Ghosh

We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…

Data Analysis, Statistics and Probability · Physics 2015-05-27 Eugene B. Postnikov , Igor M. Sokolov

Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…

Machine Learning · Statistics 2026-05-19 Issa-Mbenard Dabo , Jérémie Bigot

Spatially referenced data often have autocovariance functions with elliptical isolevel contours, a property known as geometric anisotropy. The anisotropy parameters include the tilt of the ellipse (orientation angle) with respect to a…

Statistics Theory · Mathematics 2021-10-04 Manolis P. Petrakis , Dionissios T. Hristopulos

A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…

Statistics Theory · Mathematics 2019-05-31 Debashis Ghosh , Efrén Cruz-Cortés

Performance guarantees for compression in nonlinear models under non-Gaussian observations can be achieved through the use of distributional characteristics that are sensitive to the distance to normality, and which in particular return the…

Statistics Theory · Mathematics 2017-10-03 Larry Goldstein , Xiaohan Wei

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…

Statistics Theory · Mathematics 2021-05-24 Sara Kristin Schmidt , Max Wornowizki , Roland Fried , Herold Dehling

In this paper we study the asymptotic behavior of the angular bispectrum of spherical random fields. Here, the asymptotic theory is developed in the framework of fixed-radius fields, which are observed with increasing resolution as the…

Probability · Mathematics 2011-02-11 Domenico Marinucci

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Methodology · Statistics 2014-02-05 Adel Javanmard , Andrea Montanari

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

Statistics Theory · Mathematics 2022-03-28 Federica Gerace , Bruno Loureiro , Florent Krzakala , Marc Mézard , Lenka Zdeborová

This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…

Statistics Theory · Mathematics 2024-09-25 Claudia Kirch , Alexander Meier , Renate Meyer , Yifu Tang

Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…

Statistics Theory · Mathematics 2019-07-16 Hossein Keshavarz , XuanLong Nguyen , Clayton Scott

This work investigates the performance of the final iterate produced by stochastic gradient descent (SGD) under temporally dependent data. We consider two complementary sources of dependence: $(i)$ martingale-type dependence in both the…

Statistics Theory · Mathematics 2026-01-06 Yinan Shen , Yichen Zhang , Wen-Xin Zhou

Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of…

chao-dyn · Physics 2009-10-31 Thomas Schreiber , Andreas Schmitz

A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their…

Statistical Mechanics · Physics 2015-06-24 Rafal Weron

This paper investigates the statistical properties of non-linear transformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression…

Information Theory · Computer Science 2013-05-13 Paolo Banelli

The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven…

Statistics Theory · Mathematics 2012-06-08 Ning Lin , Sergey V. Lototsky

We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…

Statistics Theory · Mathematics 2015-01-05 Po-Ling Loh