Results 1 to 10 of about 142 (132)
Edgeworth Expansions and Smoothness
Annals of Probability, 1982 We give a necessary and sufficient condition for the distribution function of $n^{-1/2} \sum^n_{i=1} X_i$, where the $X_i$ are independently identically distributed with $EX_1 = 0, EX^2_1 = 1$ and $E|X_1|^{k+3} < \infty$, to possess an Edgeworth expansion to $k$ terms. The condition is not practicable but clarifies the relation between the existence of
Bickel, P. J., Robinson, J.
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On Edgeworth Expansions in the Mixture Cases
Annals of Statistics, 1989 Let X be a random vector with at least one marginal having a lattice distribution. For a wide class of statistics which can be written as a function of means of independent copies of X, it is established in this article that the one-term Edgeworth expansion is typically the same as the usual one-term expansion in the pure nonlattice case.
Babu, G. J., Singh, K.
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Edgeworth Expansions in Nonparametric Statistics
Annals of Statistics, 1974 This is a survey of recent work on Edgeworth expansions for $(M)$ estimates, rank tests and some other statistics arising in nonparametric models. A Berry-Esseen theorem for $U$-statistics which seems to be new is also proved.
P J Bickel
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On Edgeworth Expansions with Unknown Cumulants
Annals of Statistics, 1975 In this paper a new method of approximating one distribution by another is introduced. The method is essentially a modification of the Edgeworth technique which eliminates the necessity of knowing the cumulants of the distributions involved.
Gray, H. L. +2 more
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On Edgeworth Expansions in Banach Spaces
Annals of Probability, 1981 In this paper we define a generalization of Edgeworth expansions for the expectation of functions of normalized sums of i.i.d. Banach space valued random vectors. These expansions are valid up to $0(n^{-(s - 2)/2})$ for functions with $3(s - 2)$ bounded Frechet derivatives and random vectors with finite $s^{th}$ absolute moment.
Friedrich Götze
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Chebyshev–Edgeworth-Type Approximations for Statistics Based on Samples with Random Sizes
Mathematics, 2021 Second-order Chebyshev–Edgeworth expansions are derived for various statistics from samples with random sample sizes, where the asymptotic laws are scale mixtures of the standard normal or chi-square distributions with scale mixing gamma or inverse ...
Gerd Christoph, Vladimir V. Ulyanov
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Analysis of quasi-lattice distributions of statistics from finite population
Lietuvos Matematikos Rinkinys, 2004 Edgeworth expansions are used for approximation of quantiles, estimation of parameters, construction of confidence intervals and testing hypothesis. Paper shows how to construct ` ` long'' Edgewort asymptotic expansions.
Jurgita Turkuvienė, Algimantas Bikelis
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Second Order Chebyshev–Edgeworth-Type Approximations for Statistics Based on Random Size Samples
Mathematics, 2023 This article completes our studies on the formal construction of asymptotic approximations for statistics based on a random number of observations.
Gerd Christoph, Vladimir V. Ulyanov
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Contributions to Risk Assessment with Edgeworth–Sargan Density Expansions (I): Stability Testing
Mathematics, 2022 This paper analytically derives a stability test for the probability distribution of a random variable that follows the Edgeworth–Sargan density, also called Gram–Charlier.
Ignacio Mauleón
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Edgeworth expansions for network moments
The Annals of Statistics, 2022 Network method of moments arXiv:1202.5101 is an important tool for nonparametric network inference. However, there has been little investigation on accurate descriptions of the sampling distributions of network moment statistics. In this paper, we present the first higher-order accurate approximation to the sampling CDF of a studentized network moment ...
Yuan Zhang, Dong Xia
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