International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 491-496
doi:10.1155/S0161171284000521
A remark on the r-th mean differentiability
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.
Abstract
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.