Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 3, 448--463

FITTING A SUM OF EXPONENTIALS TO EQUISPACED DATA

By

DEBASIS KUNDU and AMIT MITRA
*Indian Institute of Technology Kanpur, India*

SUMMARY. In this paper we consider fitting a sum of exponentials to equispaced data. We propose a new non iterative method to estimate the parameters, which can be used as an initial guess in any standard minimization algorithm. We use two real life data sets to see how the new estimate behaves as an initial guess for different algorithms available in the literature. It is well known (Wu; 1981) that for the exponential model any estimate is inconsistent in the usual sense, we redefine the consistency and the asymptotic normality of the least squares estimates under this new assumption.

*AMS (1991) subject classification.*62J02, 62E25 .

*Key words and phrases. *Prony's algorithm, least squares estimates, separable regression, non-linear
regression, equispaced data.