Statistical hypothesis testing for the shape of impulse response function

Iryna V. Rozora

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 6, 1459-1474

Abstract: The problem of estimation of unknown response function of a time-invariant continuous linear system is considered. Integral sample input–output cross-correlogram is taken as an estimator of the response function. The inputs are supposed to be zero-mean stationary Gaussian process. A criterion on the shape of impulse response function is given. For this purpose, we apply a theory of square–Gaussian random processes and estimate the probability that supremum of square–Gaussian process exceeds the level specified by some function.

Date: 2018
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DOI: 10.1080/03610926.2017.1321125

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