Non-parametric estimation of residual moments and covariance

Nonparametric 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...

Non-parametric Residual Variance Estimation in Supervised Learning

The residual variance estimation problem is well-known in statistics and machine learning with many applications for example in the field of nonlinear modelling. In this paper, we show that the problem can be formulated in a general supervised learning context. Emphasis is on two widely used non-parametric techniques known as the Delta test and the Gamma test. Under some regularity assumptions,...

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...

Non–parametric volatility estimation

Inference about clustering and parametric assumptions in covariance matrix estimation

Selecting an estimator for the covariance matrix of a regression’s parameter estimates is an important step in hypothesis testing. From less robust to more robust, the available choices include: Eicker/White heteroskedasticity-robust standard errors, cluster-robust standard errors, and multi-way cluster-robust standard errors. The rationale for using a less robust covariance matrix estimator is...