Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 2, pp. 277--285

RATE OF CONVERGENCE OF THE MAXIMUM LIKELIHOOD ESTIMATE OF A CHANGE-POINT

By

V.K. JANDHYALA and S.B. FOTOPOULOS, *Washington State University, Pullman, USA*

*SUMMARY. *Maximum likelihood method is applied to estimate the change-point of a parameter associated with a
sequence of independent random variables. Exact expressions are derived for the limiting distribution of the maximum
likelihood estimator of a change-point and computable bounds are suggested. Exponential rate of convergence is
obtained from finite sample to the case of infinite sample.

*AMS (1991) subject classification. *Primary 62F10; secondary 60J15, 62F12.

*Key words and phrases. *Maximum of a random walk, negative drift, maximum likelihood estimate,
parameter change.