An Upper Bound for Functions of Estimators in High Dimensions

2020/08/06 by Mehmet Caner, Xu Han, Caner, Mehmet +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Econometrics (econ.EM) #FOS: Economics and business #Risk and Portfolio Optimization #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #econ.EM

paper · pdf · doi:10.48550/arxiv.2008.02636

arxiv created 2020/08/06 · openalex publication_date 2020/08/06 · arxiv updated 2020/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge faster, slower, or at the same rate as estimators depending on the behavior of the partial derivative of the function. We illustrate this via three examples. The first two examples use the upper bound for testing in high dimensions, and third example derives the estimated out-of-sample variance of large portfolios. All our results allow for a larger number of parameters, p, than the sample size, n.

Related

• Delta Theorem in the Age of High Dimensions
• High-dimensional CLT: Improvements, Non-uniform Extensions and Large Deviations
• Improved Central Limit Theorem and bootstrap approximations in high dimensions
• On Extreme Value Asymptotics of Projected Sample Covariances in High Dimensions with Applications in Finance and Convolutional Networks
• High-Dimensional Econometrics and Regularized GMM