Consider a parametric statistical model P (dx|θ) and an improper prior distribution ν(dθ) that together yield a (proper) formal posterior distribution Q(dθ|x). The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of θ is admissible under squared error loss. Eaton [Ann. Statist. 20 (1992) 1147–1179] has shown that a sufficient condition for strong ...
Lemma 9 (Lemma 1 restated). Let h 1 ,. .. , h n−1 be an ensemble of hypotheses generated by an online learning algorithm working with a bounded loss function : H× Z × Z → [0, B]. Then for any δ > 0, we have with probability at least 1 − δ,
in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed
linear spaces and study the set of all compact operators on these spaces. then we
introduce the notions of fuzzy boundedness and investigate a new norm operators
and the relationship between continuity and boundedness. and, we show that the
space of all fuzzy bounded operators is complete. finally, we define...
