A remark on the r-th mean differentiability
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...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000521 |
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| _version_ | 1832562996191166464 |
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| author | George D. Stamatelos |
| author_facet | George D. Stamatelos |
| author_sort | George D. Stamatelos |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0c92a00bc07a401cb2d539ab92c3a633 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0c92a00bc07a401cb2d539ab92c3a6332025-02-03T01:21:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017349149610.1155/S0161171284000521A remark on the r-th mean differentiabilityGeorge D. Stamatelos0Department of Mathematics, University of Patras, GreeceThis 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.http://dx.doi.org/10.1155/S0161171284000521stochastic processderivative of r-th meanprobability measure. |
| spellingShingle | George D. Stamatelos A remark on the r-th mean differentiability International Journal of Mathematics and Mathematical Sciences stochastic process derivative of r-th mean probability measure. |
| title | A remark on the r-th mean differentiability |
| title_full | A remark on the r-th mean differentiability |
| title_fullStr | A remark on the r-th mean differentiability |
| title_full_unstemmed | A remark on the r-th mean differentiability |
| title_short | A remark on the r-th mean differentiability |
| title_sort | remark on the r th mean differentiability |
| topic | stochastic process derivative of r-th mean probability measure. |
| url | http://dx.doi.org/10.1155/S0161171284000521 |
| work_keys_str_mv | AT georgedstamatelos aremarkontherthmeandifferentiability AT georgedstamatelos remarkontherthmeandifferentiability |