
Error bounds for overdetermined and underdetermined generalized centred simplex gradients
Using the Moore–Penrose pseudoinverse, this work generalizes the gradien...
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Behaviour of Familywise Error Rate in Normal Distributions
We study the behaviour of the familywise error rate (FWER) for Bonferron...
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Error bounds for the normal approximation to the length of a Ewens partition
Let K(=K_n,θ) be a positive integervalued random variable whose distrib...
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On the limiting distribution of sample central moments
We investigate the limiting behavior of sample central moments, examinin...
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Lonely Points in Simplices
Given a lattice L in Z^m and a subset A of R^m, we say that a point in A...
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The Asymptotic Generalized PoorVerdu Bound Achieves the BSC Error Exponent at Zero Rate
The generalized PoorVerdu error lower bound for multihypothesis testing...
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The complex behaviour of Galton rank order statistic
Galton's rank order statistic is one of the oldest statistical tools for...
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Limiting behaviour of the generalized simplex gradient as the number of points tends to infinity on a fixed shape in R^n
This work investigates the asymptotic behaviour of the gradient approximation method called the generalized simplex gradient (GSG). This method has an error bound that at first glance seems to tend to infinity as the number of sample points increases, but with some careful construction, we show that this is not the case. For functions in finite dimensions, we present two new error bounds ad infinitum depending on the position of the reference point. The error bounds are not a function of the number of sample points and thus remain finite.
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