Adaptive covariance estimation of locally stationary processes

• 成果类型: Article
• 署名作者: Mallat, S; Papanicolaou, G; Zhang, ZF
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1-47
• 关键词: NONSTATIONARY

摘要

It is shown that the covariance operator of a locally stationary process has approximate eigenvectors that are local cosine functions. We model locally stationary processes with pseudo-differential operators that are time-varying convolutions. An adaptive covariance estimation is calculated by searching first for a best local cosine basis which approximates the covariance by a band or a diagonal matrix. The estimation is obtained from regularized versions of the diagonal coefficients in the best basis.