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On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
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Albert Y. Lo
Published/Copyright:
February 25, 2010
Abstract
An asymptotic expansion for the approximation of standardized products of large numbers of smooth positive functions by exp(–𝑥2/2) is given. This result is closely related to the Bernstein–von Mises theorem on the normal approximation of posterior distributions.
Key words and phrases:: Approximation of large products of functions; Bernstein–von Mises theorem
Received: 2000-12-25
Published Online: 2010-02-25
Published in Print: 2001-June
© Heldermann Verlag
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Keywords for this article
Approximation of large products of functions;
Bernstein–von Mises theorem
Articles in the same Issue
- 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
