Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 1 ,pp. 62--71

EXTENSIONS OF CONSISTENCY RESULTS RELATED TO THE STOCHASTIC ORDER

By

J.A. CUESTA-ALBERTOS Universidad de Cantabria, Spain
and
C. MATR\'AN Universidad de Valladolid, Spain

SUMMARY.We present a very simple methodology, based on the use of the quantile transformation, which easily leads to the relaxation of the identical distribution assumption in several consistency results.

AMS (1991) subject classification.60F15, 62F12.

Key words and phrases. Consistency, strong law of large numbers, non identically distributed random variables, stochastic order, M-estimators,F-means, weighted sums, Banach spaces.

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