期刊
ANNALS OF STATISTICS
卷 41, 期 4, 页码 1816-1864出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/13-AOS1128
关键词
Large matrix estimation; measurement error; minimax lower bound; multi-scale; optimal convergence rate; sparsity; subGaussian tail; threshold; volatility matrix estimator
资金
- NSF [DMS-10-5635, DMS-12-65203]
- NSF Career Award [DMS-0645676]
- NSF FRG [DMS-08-54975]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1265203] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1005635] Funding Source: National Science Foundation
Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a high-dimensional Ito process observed with measurement errors at discrete time points. The minimax rate of convergence is established for estimating sparse volatility matrices. By combining the multi-scale and threshold approaches we construct a volatility matrix estimator to achieve the optimal convergence rate. The minimax lower bound is derived by considering a subclass of Ito processes for which the minimax lower bound is obtained through a novel equivalent model of covariance matrix estimation for independent but nonidentically distributed observations and through a delicate construction of the least favorable parameters. In addition, a simulation study was conducted to test the finite sample performance of the optimal estimator, and the simulation results were found to support the established asymptotic theory.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据