Quantile Process with Applications : Chirp Signal Model

The parameters in the well-known chirp signal model controls the frequency fluctuations of the signals, and consequently, the estimation of the parameters has received considerable attention in the literature of statistical signal processing. In the same spirit with a broader view, this article investigates the quantile estimator of parameters involved in the chirp signal model, which enables us to provide basic features of the entire distribution of the signals. In the course of this study, we establish the limiting behaviour of the associated stochastic process, which we call quantile process. As the applications of this result, we obtain the limiting distributions of various quantile based measures of descriptive statistics, which give us summarized features of the fluctuations of the signals in various senses. Finally, along with extensive simulation study, the practicability of the proposed methodology is shown on a few benchmark real datasets closely related with various chirp signal models.