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Related papers: Fr\'echet Analysis Of Variance For Random Objects

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We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasi-arithmetic means are allowed to be…

Statistics Theory · Mathematics 2022-05-09 Yuichi Akaoka , Kazuki Okamura , Yoshiki Otobe

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

Statistics Theory · Mathematics 2023-04-19 Taras Bodnar , Stepan Mazur , Nestor Parolya

Finite Sample Smeariness (FSS) has been recently discovered. It means that the distribution of sample Fr\'echet means of underlying rather unsuspicious random variables can behave as if it were smeary for quite large regimes of finite…

Statistics Theory · Mathematics 2021-03-02 Benjamin Eltzner , Shayan Hundrieser , Stephan F. Huckemann

We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…

Mathematical Physics · Physics 2011-01-18 Mariya Shcherbina

The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…

Methodology · Statistics 2024-03-28 Lu Lin , Ze Chen

This paper is concerned with inference based on the mean function of a functional time series, which is defined as a collection of curves obtained by splitting a continuous time record, e.g. into daily or annual curves. We develop a normal…

Statistics Theory · Mathematics 2011-05-03 Lajos Horvath , Piotr Kokoszka , Ron Reeder

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…

Computation · Statistics 2008-12-18 Marie Chavent , Jérôme Saracco

The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

This paper provides a framework for estimating the mean and variance of a high-dimensional normal density. The main setting considered is a fixed number of vector following a high-dimensional normal distribution with unknown mean and…

Methodology · Statistics 2019-05-07 Shyamalendu Sinha , Jeffrey D. Hart

Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many…

Methodology · Statistics 2020-07-23 Alexander Petersen , Xi Liu , Afshin A. Divani

In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…

Probability · Mathematics 2022-01-12 Mario Diaz , James A. Mingo

A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…

Methodology · Statistics 2016-09-30 Norm Matloff

Stochastic gradient algorithms are more and more studied since they can deal efficiently and online with large samples in high dimensional spaces. In this paper, we first establish a Central Limit Theorem for these estimates as well as for…

Statistics Theory · Mathematics 2017-10-17 Antoine Godichon-Baggioni

Random Effects analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation in the study group since in…

Applications · Statistics 2013-09-03 Jonathan D. Rosenblatt , Matthijs Vink , Yoav Benjamini

Distribution-as-response regression problems are gaining wider attention, especially within biomedical settings where observation-rich patient specific data sets are available, such as feature densities in CT scans (Petersen et al., 2021)…

Computation · Statistics 2025-12-22 Alexander Coulter , Rebecca Lee , Irina Gaynanova

For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…

Statistics Theory · Mathematics 2008-10-10 T. Royen

We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency…

Statistics Theory · Mathematics 2016-02-02 Peter M. Aronow , Forrest W. Crawford , José R. Zubizarreta

We propose a novel test for assessing partial effects in Frechet regression on Bures Wasserstein manifolds. Our approach employs a sample splitting strategy: the first subsample is used to fit the Frechet regression model, yielding…

Machine Learning · Statistics 2025-07-01 Haoshu Xu , Hongzhe Li

A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…

Probability · Mathematics 2023-12-25 Thomas Anton , Sutanuka Roy , Rabee Tourky