ON THE NONPARAMETRIC-ESTIMATION OF COVARIANCE FUNCTIONS
成果类型：
Article
署名作者：
HALL, P; FISHER, NI; HOFFMANN, B
署名单位：
Commonwealth Scientific & Industrial Research Organisation (CSIRO)
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176325774
发表日期：
1994
页码：
2115-2134
关键词：
摘要：
We describe kernel methods for estimating the covariance function of a stationary stochastic process, and show how to ensue that the estimator has the positive semidefiniteness property. From a practical viewpoint, our method is significant because it does not demand a parametric model for covariance. From a technical angle, our results exhibit a striking departure from those in more familiar cases of kernel estimation. For example, in the context of covariance estimation, kernel estimators can have the same convergence rates as maximum likelihood estimators, and can have exceptionally fast convergence rates when employed to estimate variance.