By R. Bahadur
Книга a few restrict Theorems in information a few restrict Theorems in facts Книги Математика Автор: R. R. Bahadur Год издания: 1987 Формат: pdf Издат.:Society for commercial arithmetic Страниц: forty eight Размер: 2,1 Mb ISBN: 0898711754 Язык: Английский0 (голосов: zero) Оценка:A dialogue of a few subject matters within the concept of huge deviations corresponding to moment-generating services and Chernoff's theorem, and of elements of estimation and trying out in huge samples, equivalent to precise slopes of try out facts.
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Remark 3. 6) holds with some / is always nontrivial, and §§ 1-5 discus exactly this problem. 2 shows that if (somehow) the exact slope of {7^,} is known, then asymptotic estimates of 1 — Fn(nl/2t) become available. Some examples of this method of estimating large deviation probabilities are given in [Bll]. 3. 5) hold for each ^ b(9) ^ oo and 0 ^ c(9) ^ oo. Then, for any t such that are well-defined, Proof. 7). Let 9e&1 be a point such that b(9) > r; by hypothesis, there are such points 9. 5) imply that there are such sequences s.
L. estimate of P0(B) is Pon(B) = Qn(B), say; Qn is, of course, a probability measure in the set (J?. l. method always estimates the entire under lying distribution from given data. l. , if some P in ^ obtains, then Qn -> P with probability one. , a functional on ^, and if so whether this functional is continuous on &. It seems reasonable not to confound such nonstochastic questions with the consistency problem, so we dispense with parametrization; more precisely, we take P itself to be the unknown parameter and 3P to be the parameter space.
If we redefine fg(x) to be 1/0 for 0 < x <; 0 and fe(x) = 0 for x > 9, then Conditions A-E are satisfied. Note. This section is based mainly on [W2] and partly on [Bl], [B8], [B9], [Kl], and [R2] (cf. [PI] for further discussion and additional references). SOME LIMIT THEOREMS IN STATISTICS 37 10. The exact slope of the likelihood ratio statistic. In this section we con- sider the framework (A", $}, ^, /i, {fp: P e &} described at the beginning of § 9. Let ,^0 be a given nonempty proper subset of & and consider the null hypothesis that some P in ^0 obtains.
