Abstract
Normalized differences of several adjacent observations, referred to as pseudo-measurement errors in this paper, are used in so-called difference-based estimation methods as building blocks for the variance estimate of measurement errors. Numerical results demonstrate that pseudo-measurement errors can be used to serve the role of measurement errors. Based on this information, we propose the use of pseudo-measurement errors to determine an appropriate statistical model and then to subsequently investigate whether there is a mathematical model misspecification or error. We also propose to use the information provided by pseudo-measurement errors to quantify uncertainty in parameter estimation by bootstrapping methods. A number of numerical examples are given to illustrate the effectiveness of these proposed methods.
Funding source: Air Force Office of Scientific Research
Award Identifier / Grant number: AFOSR FA9550-12-1-0188
Funding statement: This research was supported in part by the Air Force Office of Scientific Research under grant number AFOSR FA9550-12-1-0188, and in part by the US Department of Education Graduate Assistance in Areas of National Need (GAANN) under grant number P200A120047.
The authors wish to gratefully acknowledge the efforts of two referees of an earlier version of this manuscript whose questions and suggestions resulted in significant improvements of the current manuscript.
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