Optimal Estimation of Variance from Uniformly-spaced Data

• Activity Number: 402
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Thomas Bzik*+
• Companies: Air Products and Chemicals
• Keywords: Variance ; Time ; Distance ; Contiguous ; Sequence

Abstract

Variance often is studied as a function of time or distance from data that has been collected at uniform intervals. There are multiple ways of estimating the variance of the duration or length of contiguous measurement subsequence. One approach, for each duration or length, is to define as many nonoverlapping, contiguous sequences of size n from the N contiguous total measurements and pool the variance estimates. For many combinations of n and N, this approach will not provide a unique result because some measurements are not used in the estimation process. An alternative is to use all the data by estimating the variance from all possible contiguous sequences of size n from the N contiguous measurements and pool the variance estimates. This approach does provide a unique result and, typically, more precise variance estimates. Improved precision arises from the fullest possible data use. In some circumstances, improved precision does not result due to relative data over or underutilization that can offset the benefit of full data usage. An adaptation of the all-possible-contiguous sequence estimation approach resolves this issue for all combinations of n and N.