International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 491-496

A remark on the r-th mean differentiability

George D. Stamatelos

Department of Mathematics, University of Patras, Greece

Received 11 January 1983; Revised 9 May 1983

Copyright © 1984 George D. Stamatelos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the r-th mean differentiability. In the mathematical developments regarding the asymptotic expansion and the asymptotic distribution of the likelihood function, there arises the question whether the assumptions made on the model imply differentiability in the r-th mean of the underlying random functions, for integer values r<r. The present paper provides an answer to this question and also gives the explicit form of the derivatives in the r-th mean involved.