Testing composite hypotheses via convex duality
نویسندگان
چکیده
منابع مشابه
Testing Composite Hypotheses via Convex Duality ∗
We study the problem of testing composite hypotheses versus composite alternatives, using a convex duality approach. In contrast to classical results obtained by Krafft & Witting [11], where sufficient optimality conditions are obtained via Lagrange duality, we obtain necessary and sufficient optimality conditions via Fenchel duality under some compactness assumptions. This approach also differ...
متن کاملOn Sequential Hypotheses Testing via Convex Optimization
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [1]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector of parameters underlying the distribution of observations belongs to a convex set. The nearly optimal under appropriate conditions test is yielded by a solutio...
متن کاملDiscussion of “ Hypotheses testing by convex optimization ” ∗
We congratulate the authors on a stimulating paper on a very intuitive and general approach to construct hypotheses tests. Restricting the considered class of tests to simple ones determined by a detector function φ, it seems most natural to minimize over φ and maximize over the pair (x, y) ∈ X ×Y where X is the hypothesis and Y the alternative. Particularly, this guarantees that the correspond...
متن کاملTesting composite hypotheses about discrete ergodic processes
Given a discrete-valued sample X1, . . . ,Xn, we wish to decide whether it was generated by a distribution belonging to a family H0, or it was generated by a distribution belonging to a family H1. In this work we assume that all distributions are stationary ergodic and do not make any further assumptions (in particular, no independence or mixing rate assumptions). We find some necessary and som...
متن کاملGeneralized Neyman-pearson Lemma via Convex Duality
We extend the classical Neyman-Pearson theory for testing composite hypotheses versus composite alternatives, using a convex duality approach as in Witting (1985). Results of Aubin & Ekeland (1984) from non-smooth convex analysis are employed, along with a theorem of Komlós (1967), in order to establish the existence of a max-min optimal test in considerable generality, and to investigate its p...
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: Bernoulli
سال: 2010
ISSN: 1350-7265
DOI: 10.3150/10-bej249