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Statistical Methods Related to the Law of the Iterated Logarithm

Herbert Robbins
- 01 Oct 1970 - 
- Vol. 41, Iss: 5, pp 1397-1409
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TLDR
In this article, a method for obtaining probability inequalities and related limit theorems concerning the behavior of the entire sequence of random variables with a specified joint probability distribution is given. But the method is not suitable for the case of the random variables in the case where the distribution of the variables is fixed.
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Detection of abrupt changes: theory and application

TL;DR: A unified framework for the design and the performance analysis of the algorithms for solving change detection problems and links with the analytical redundancy approach to fault detection in linear systems are established.
Journal Article

On the complexity of best-arm identification in multi-armed bandit models

TL;DR: This work introduces generic notions of complexity for the two dominant frameworks considered in the literature: fixed-budget and fixed-confidence settings, and provides the first known distribution-dependent lower bound on the complexity that involves information-theoretic quantities and holds when m ≥ 1 under general assumptions.

Sequential analysis: some classical problems and new challenges

Tze Leung Lai
TL;DR: A brief review of the developments in several classical problems of sequential analysis and their applications to biomedicine, economics and engi- neering can be found in this paper.
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A fully sequential procedure for indifference-zone selection in simulation

TL;DR: The procedures presented are appropriate when it is possible to repeatedly obtain small, incremental samples from each simulated system and are based on the assumption of normally distributed data, so the impact of batching is analyzed.
References
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Book

Testing statistical hypotheses

TL;DR: The general decision problem, the Probability Background, Uniformly Most Powerful Tests, Unbiasedness, Theory and First Applications, and UNbiasedness: Applications to Normal Distributions, Invariance, Linear Hypotheses as discussed by the authors.
Journal ArticleDOI

Boundary Crossing Probabilities for the Wiener Process and Sample Sums

TL;DR: In this paper, it was shown that the probability that S n is the nth partial sum of any sequence x 1, x 2, x 3 of independent and identically distributed (i.i.d.) random variables with mean 0 and variance 1.
Journal ArticleDOI

Iterated logarithm inequalities.

TL;DR: A sequence of independent, identically distributed random variables with mean 0, variance 1, and moment generating function ϕ(t) = E(etz) finite in some neighborhood of t= 0 is introduced.