כתבה
arXiv cs.LG ·
אופטימליות סדר-תנאית של גבול Gaffke
On the Order-Conditional Optimality of Gaffke's Bound
Gaffke's bound הוא אופטימלי לפרמטר הממוצע המרבי. המחקר מראה כי אין LCB אחר שיכול לשפר על Gaffke's bound.
תקציר מקורי באנגליתarXiv:2607.22971v2 Announce Type: cross Abstract: Let $X = (X_1, \ldots, X_n)$ be a random vector from any Borel probability law on $\mathbb{R}_+^n$. We revisit the problem of deriving a lower confidence bound (LCB) on a scalar parameter of that law. We recast classical work, beginning with Buehler, in purely probabilistic terms to form a more accessible and extensible framework. We then specialize the framework to the case where the components of $X$ are independent. In this context, we prove that Gaffke's bound is Buehler optimal for the order that it induces with respect to the maximum marginal mean parameter: $max_{i \in [n]} E_Q[X_i]$, which reduces to the common mean when the $X_i$ are independent and identically distributed. That is to say, no other valid LCB that orders samples in
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arxiv.org
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