Statistical Methods Related to the Law of the Iterated Logarithm
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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.Citations
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Detection of abrupt changes: theory and application
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A fully sequential procedure for indifference-zone selection in simulation
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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
Confidence sequences for mean, variance, and median.
D. A. Darling,Herbert Robbins +1 more
Journal ArticleDOI
Iterated logarithm inequalities.
D. A. Darling,Herbert Robbins +1 more
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.