Confidence and Tolerance Regions for the Signal Process

Abstract

Iterative schemes play a dominant role in evaluating parameters in statistics. Sequences and iterations are related to the signal process. The first order autoregressive model is discussed. The problem of evaluating confidence intervals for the involved parameter is discussed and a simulation approach is provided. Eventually, within the interval (-1,1) the estimated coverage is very close to the nominal level. Different small sample sizes provide evidence that the method performs well, minimizing uncertainty. The contribution of this paper concerns: (i) The confidence interval for the signal process even in the case of such a small sample that provides coverage (1-α)100% despite the theoretical problems, and (ii) The tolerance region introduced performs well with sample size n = 10 , while it is accepted for applications with sample size n = 5 . Patents related to topic have been discussed. Keywords: Sequential procedure, signal process, autoregressive model, confidence interval, tolerance region, autoregressive error, Hierarchical Networks, Model–Oriented Design and Analysis, symmetric tolerance regions, computation, Mean Square Error, D–optimal design, discrete time system, Fisher’s information matrix