Optimal-Partitioning Inequalities in Classification and Multi-Hypotheses Testing
نویسندگان
چکیده
منابع مشابه
Optimal-partitioning Inequalities in Classification and Multi-hypotheses Testing
Optimal-partitioning a dminimax risk inequalities are obtained for the classification and multi-hypotheses t ting problems. Best possible bounds are derived for the minimax risk for location parameter families, based on the tail concentrations and Levy concentrations of the distributions. Special attention is given to continuous distributions with the maximum likelihood ratio property and to sy...
متن کاملOptimal Testing of Equivalence Hypotheses
In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X1, . . . ,Xn are i.i.d. with distribution Pθ, with θ ∈ R . Let g(θ) be some real-valued parameter of interest. The null hypothesis asserts g(θ) / ∈ (a, b) versus the alternative g(θ)∈ (a, b). For example, such hypotheses occur in bioequivalence studies where one may wish to show two drug...
متن کاملStability Estimating in Optimal Sequential Hypotheses Testing
We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X1, X2, . . . when testing two simple hypotheses about their common density f : f = f0 versus f = f1. As a functional to be minimized, it is used a weighted sum of the average (under f0) sample number and the two types error probabilities. We prove that the...
متن کاملOptimal-partitioning Inequalities for Nonatomic Probability Measures
Suppose fix,... ,fin are nonatomic probability measures on the same measurable space (S, S). Then there exists a measurable partition isi}"=i of 5 such that Pi(Si) > (n + 1 M)'1 for a11 i l,...,n, where M is the total mass of V?=i ßi (tne smallest measure majorizing each m). This inequality is the best possible for the functional M, and sharpens and quantifies a well-known cake-cutting theorem ...
متن کاملTesting fuzzy hypotheses with vague data
The problem of testing fuzzy hypotheses in the presence of vague data is considered. A new method based on the necessity index of strict dominance (NSD) is suggested. An example hoe to apply the proposed test in statistical quality control is shown.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1989
ISSN: 0090-5364
DOI: 10.1214/aos/1176347272