Signal model specification testing via kernel reconstruction methods

Given noisy samples of a signal, the problem of testing whether the signal belongs to a given parametric class of signals is considered. We examine the nonparametric situation as for a well-defined null hypothesis signal model we admit broad alternative signal classes that cannot be parametrized. For such a setup, we introduce testing procedures relying on nonparametric kernel-type sampling reconstruction algorithms properly adjusted for noisy data. The proposed testing procedure utilizes the L₂ - distance between the kernel estimate and signals from the parametric target class. The central limit theorem of the test statistic is derived yielding a consistent testing method. Hence, we obtain the testing algorithm with the desirable level of the probability of false alarm and the power tending to one.