Covariance estimation for distributions with ${2+\varepsilon}$ moments
نویسندگان
چکیده
منابع مشابه
Covariance Estimation for Distributions with 2 + Ε Moments
We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound N = O(n) for every distribution whose k-dimensional marginals have uniformly bounded 2+ε moments outside the sphere of radius O( √ k). In the specific case...
متن کاملNonparametric Estimation of Residual Moments and Covariance
Abstract: The aim of nonparametric regression is to model the behaviour of a response vector Y in terms of an explanatory vector X , based only on a finite set of empirical observations. This is usually performed under the additive hypothesis Y = f(X) + R, where f(X) = E(Y |X) is the true regression function and R is the true residual variable. Subject to a Lipschitz condition on f , we propose...
متن کاملInformation Covariance Matrices for Multivariate Burr III and Logistic Distributions
Main result of this paper is to derive the exact analytical expressions of information and covariance matrices for multivariate Burr III and logistic distributions. These distributions arise as tractable parametric models in price and income distributions, reliability, economics, Human population, some biological organisms to model agricultural population data and survival data. We showed that ...
متن کاملEstimation of the covariance structure of heavy-tailed distributions
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance matrices corresponding to sub-Gaussian distributions is well-understood, much less in known in the case of heavy-tailed data. As K. Balasubramanian and M. Yu...
متن کاملEstimation of Distributions , Moments and Quantiles in Deconvolution Problems
When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample, since we do not have a sample from the target. These and other considerations motivate the development of estimators of distributions, and of related quantities such as moments and quantiles, in errors-in-variables settings. We show that such estim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2013
ISSN: 0091-1798
DOI: 10.1214/12-aop760