By J. Kožešnik (auth.)
The 9th Prague convention on details thought, Statistical determination services, and Random approaches used to be prepared via the Institute of knowledge concept and Automation of the Czechoslovak Academy of Sciences from June 28 to July 2, 1982. equally because the previous Prague meetings, in the course of their twenty six years histo ry, it supplied an area for the presentation and dialogue of modern medical effects, in addition to for private contacts of many scien tists either from in a foreign country and from Czechoslovakia. approximately a hundred and fifty precise ists from 17 nations participated within the convention and so they learn greater than a hundred papers (including 18 invited ones), 88 of which were released within the current volumes of the Transactions of the convention. specifically invited papers, having been learn by means of extraordinary experts, have introduced necessary supply for contributors to create themselves an orientation within the glossy developments of the above point out ed clinical branches. let us use this chance to precise our honest because of all who've contributed to the good fortune of the convention, espe cially to people who ready and offered papers. Our gratitude is additionally as a result of Academician Jaroslav Kozesnik, the clinical editor of the Transactions, and to the editorial board for reviewing all papers and satisfying many printing deal with ment tasks. we want to understand a superb paintings of all colleagues from the Institute of data concept and Automation, who participated within the practise and within the association of the Conference.
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For instance, . :: DR since Hi ~ Hi' SOME SPECIAL RESULTS CONCERNING MODELS (I) AND (II) That the composite statistical hypotheses of the £-contaminated model (I) are convex sets it is immediate. As to those of the f-divergence like neighborhood model (II), their convexity may be proved as follows: Let Q'1,Q'2, ... :: since the function g(u) := uf(l) is convex for u~ (O,~): Assuming u that f has a second derivative we, namely, obtain g I (u) g"(u) since f(v) is, by assumption, convex. D. " " Model (I).
Then there exists a natural number Cl(E,U), independent of n, such that KUCE/n) S clCE,U) for all nEN. Moreover, if C(InE)<~' then there exists a natural number c(U), dependent only on U, such that Ku(E/n) S 2C ( In E) + c(u). u Proof. According to Theorem 2 there exists, for each EcI indicable by an effective digital indicator, a natural number no=no(E) such that E can be written as a union of at most 2n o disjoint intervals of the form I(j,2 nO ). Hence, E is uniquely determined by n the sequence e(2 o,E) which ascribes units just to the intervals belonging to E.
1\ A MDR-LFP (Ql,Q2) for the e;-contamination Huber's THEOREM S. 16) for a LFP obtained in [3]. Remark. In [3], however, as we know it is nothing said on the interesting property (22) of the solution obtained for the LFP. , " Model II. ,Q~) and for MDR-LFP (Ql,Q2)' As in the case of model (I), for establishing these equations we are based on Theorems 3 and 2, respectively. As said in the introduction, for the constrained minimizations needed the extremal generalized f-entropy method, introduced in [2], is applied.