Sampling designs for estimation of a random process

Yingcai Su and Stamatis Cambanis

Stochastic Processes and their Applications, 1993, vol. 46, issue 1, 47-89

Abstract: A random process X(t), t[epsilon][0,1], is sampled at a finite number of appropriately designed points. On the basis of these observations, we estimate the values of the process at the unsampled points and we measure the performance by an integrated mean square error. We consider the case where the process has a known, or partially or entirely unknown mean, i.e., when it can be modeled as X(t) = m(t) + N(t), where m(t) is nonrandom and N(t) is random with zero mean and known covariance function. Specifically, we consider (1) the case where m(t) is known, (2) the semiparametric case where m(t) = [beta]1[latin small letter f with hook]1(t)+...+[beta]q[latin small letter f with hook]fq(t), the [beta]i's are unknown coefficients and the [latin small letter f with hook]i's are known regression functions, and (3) the nonparametric case where m(t) is unknown. Here fi(t) and m(t) are of comparable smoothness with the purely random part N(t), and N(t) has no quadratic mean derivative. Asymptotically optimal sampling designs are found for cases (1), (2) and (3) when the best linear unbiased estimator (BLUE) of X(t) is used (a nearly BLUE in case (3)), as well as when the simple nonparametric linear interpolator of X(t) is used. Also it is shown that the mean has no effect asymptotically, and several examples are considered both analytically and numerically.

Keywords: sampling; designs; interpolation; of; random; processes; effect; of; the; mean (search for similar items in EconPapers)
Date: 1993
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(93)90085-I
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:46:y:1993:i:1:p:47-89

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().