Parameter Estimation for Nongaussian Processes via Second and Third Order Spectra with an Application to Some Endocrine Data

Abstract

Quite a variety of processes that are observed in biomedicine have a pulse-like character and with bursts of activity occurring every so often with the principal variation corresponding to the location and size of the activity. Figure 1 provides examples of the temporal variation of the level of concentration of a particular hormone in the blood stream of a cow. One analytic representation for such processes is provided by

$$ Y(t) = \,\sum\limits_j {{A_j}} \,a(t - {\sigma _j})$$

((1))

with the Gj the times of initiation of pulses, with the Aj the respective amplitudes of the pulses and with a (r) providing the pulse shape.