Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 312--320

ON ASYMPTOTIC DISTRIBUTION OF GENERALIZED $M$-ESTIMATES

By

J. K. GHOSH, S. N. JOSHI, *Indian Statistical Institute*

SUMMARY. Let {$X_n (t)$} be a sequence of stochastic processes with continuous paths. In this note, the asymptotic distribution of a suitably chosen root of $X_n (t) =0$ is investigated. This leads to asymptotic distribution of $M$-estimates.

*AMS (1990) subject classification.* 62F12, 60K10, 62E20

*Key words and phrases*. $M$-estimates, asymptotic distribution, stochastic processes