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On Accuracy of Improved χ2-Approximations
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V. V. Ulyanov
Veröffentlicht/Copyright:
25. Februar 2010
Abstract
For a statistic S whose distribution can be approximated by χ2-distributions, there is a considerable interest in constructing improved χ2-approximations. A typical approach is to consider a transformation T = T(S) based on the Bartlett correction or a Bartlett type correction. In this paper we consider two cases in which S is expressed as a scale mixture of a χ2-variate or the distribution of S allows an asymptotic expansion in terms of χ2-distributions. For these statistics, we give sufficient conditions for T to have an improved χ2-approximation. Furthermore, we present a method for obtaining its error bound.
Key words and phrases:: Asymptotic expansion; error bound; improved χ2-approximations; scale mixture of χ2-variate; transformation
Received: 2000-12-15
Published Online: 2010-02-25
Published in Print: 2001-June
© Heldermann Verlag
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- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
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- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
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- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
- On Accuracy of Improved χ2-Approximations
- Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
Schlagwörter für diesen Artikel
Asymptotic expansion;
error bound;
improved χ2-approximations;
scale mixture of χ2-variate;
transformation
Artikel in diesem Heft
- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
- Entropy Numbers of Certain Summation Operators
- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
- Probability Measures with Big Kernels
- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
- On Accuracy of Improved χ2-Approximations
- Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
