ﻻ يوجد ملخص باللغة العربية
In this paper, we study sequential testing problems with emph{overlapping} hypotheses. We first focus on the simple problem of assessing if the mean $mu$ of a Gaussian distribution is $geq -epsilon$ or $leq epsilon$; if $muin(-epsilon,epsilon)$, both answers are considered to be correct. Then, we consider PAC-best arm identification in a bandit model: given $K$ probability distributions on $mathbb{R}$ with means $mu_1,dots,mu_K$, we derive the asymptotic complexity of identifying, with risk at most $delta$, an index $Iin{1,dots,K}$ such that $mu_Igeq max_imu_i -epsilon$. We provide non asymptotic bounds on the error of a parallel General Likelihood Ratio Test, which can also be used for more general testing problems. We further propose lower bound on the number of observation needed to identify a correct hypothesis. Those lower bounds rely on information-theoretic arguments, and specifically on t
This paper considers the change-point problem for finite sequences of networks. To avoid the difficulty of computing the normalization coefficient, such as in Exponential random graphical models (ERGMs) and Markov networks, we construct a finite meas
We present a geometrical method for analyzing sequential estimating procedures. It is based on the design principle of the second-order efficient sequential estimation provided in Okamoto, Amari and Takeuchi (1991). By introducing a dual conformal cu
For some variants of regression models, including partial, measurement error or error-in-variables, latent effects, semi-parametric and otherwise corrupted linear models, the classical parametric tests generally do not perform well. Various modificat
We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop strategy, which we prove to be asymptoticall
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical likelihood (EL)