Efficiency of linear predictors for periodic processes using an incorrect covariance function

✍ Scribed by Michael L. Stein

• Book ID: 104340268
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 493 KB
• Volume: 58
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(96)00088-2

✦ Synopsis

Previous work by the author showed that for interpolating a weakly stationary random field, using an incorrect spectral density that has similar high-frequency behavior as the correct spectral density can yield asymptotically optimal linear predictions as the number of observations in a fixed domain increases. However, explicit results on how fast this convergence to optimality occurs could only be obtained for a limited class of processes in one dimension. By considering periodic processes, this work obtains explicit rates of convergence for a broad class of processes in any number of dimensions. These results suggest analogous ones for stationary processes.