Predicting integrals of random fields using observations on a lattice
成果类型：
Article
署名作者：
Stein, ML
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1995
页码：
1975-1990
关键词：
摘要：
For a stationary random field Z on R(d), this work studies the asymptotic behavior of predictors of integral v(x)Z(x) dx based on observations on a lattice as the distance between neighbors in the lattice tends to 0. Under a mild condition on the spectral density of Z, an asymptotic expression for the mean-squared error of a predictor of integral v(x)Z(x) dx based on observations on an infinite lattice is derived. For predicting integrals over the unit cube, a simple predictor based just on observations in the unit cube is shown to be asymptotically optimal if v is sufficiently smooth and Z is not too smooth. Modified predictors extend this result to smoother processes.