Multiple hypothesis testing for time-varying nonlinear system identification

In this paper we consider the identification of a time-varying quadratic Volterra model. In the model, a set of known basis sequences are used to approximate the time-variation of the true system to enable identification. To reduce the number of parameters in the model we wish to determine which sequences can be considered significant in this approximation. The Bonferroni multiple hypothesis testing procedure is used for the selection of individual basis sequences to include in the model. This is compared with treating the multiple hypotheses separately. Not only does the Bonferroni procedure allow strong control over the false alarm but has more power when selecting the true model in low noise