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Maximum entropy and the Edgeworth expansion
IEEE Information Theory Workshop, 2005., 2005For sums of i.i.d. random variables the maximum entropy distribution with respect to the first moments fixed is compared with the Edgeworth expansion. It is demonstrated that the Edgeworth expansion can and shall be considered as a linear extrapolation of the maximum entropy distribution.
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Interpretation and manipulation of Edgeworth expansions
Annals of the Institute of Statistical Mathematics, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Onm-dependence and Edgeworth expansions
Annals of the Institute of Statistical Mathematics, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1990
Let Q be a probability measure on (ℝ k ,B k ), B k denoting the Borel sigmafield on ℝ k . Assume that the s — th absolute moment of Q is finite, $$ {\rho_s}: = \int {{{\left\| x \right\|}^s}Q(dx) < \infty } $$ (1.1) , for some integer s ≥ 3, and that Q is normalized, $$ \int {{x^{{(i)}}}Q(dx) = 0(1 \leqslant i \leqslant k)}, \int {{x^{{(i)
Rabi Bhattacharya, Manfred Denker
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Let Q be a probability measure on (ℝ k ,B k ), B k denoting the Borel sigmafield on ℝ k . Assume that the s — th absolute moment of Q is finite, $$ {\rho_s}: = \int {{{\left\| x \right\|}^s}Q(dx) < \infty } $$ (1.1) , for some integer s ≥ 3, and that Q is normalized, $$ \int {{x^{{(i)}}}Q(dx) = 0(1 \leqslant i \leqslant k)}, \int {{x^{{(i)
Rabi Bhattacharya, Manfred Denker
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Edgeworth Expansions and the Bootstrap
2016This chapter outlines the proof of the validity of a properly formulated version of the formal Edgeworth expansion, and derives from it the precise asymptotic rate of the coverage error of Efron’s bootstrap. A number of other applications of Edgeworth expansions are outlined.
Rabi Bhattacharya +2 more
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EDGEWORTH AND SADDLEPOINT EXPANSIONS FOR NONLINEAR ESTIMATORS
Econometric Theory, 2013Simple methods are developed for deriving Edgeworth, saddlepoint, and related expansions for the estimators of multivariate and nonlinear models. Illustrations are provided. Simulations are reported indicating the methods work well compared to standard asymptotic and bootstrapped approaches.
Kundhi, Gubhinder, Rilstone, Paul
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Bootstrp and Edgeworth Expansion
1990Suppose that T(P) is a functional, say real valued, on some subset P of the set of all probability measures on a measurable space (χ, B), and one wishes to obtain a confidence interval for T(P) based on n i.i.d. observations X 1 ,..., X n with common distribution P.
Rabi Bhattacharya, Manfred Denker
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Confidence Regions Based on Edgeworth Expansion
Communications in Statistics - Simulation and Computation, 2009We describe a procedure for constructing accurate confidence regions by first expanding the sampling distribution of parameter estimators in an Edgeworth series, then eliminating the beyond-normal terms by a simple polynomial transformation. We demonstrate this using the two-parameter Cauchy and Weibull distributions.
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Edgeworth expansion in partial linear models
Acta Mathematica Sinica, 1998Summary: Under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of \(\beta\) in partial linear models is given. Then a non-residual type of consistent estimation for the error variance is constructed, and finally an Edgeworth expansion for the corresponding studentized version is presented.
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Principles of Edgeworth Expansion
1992In this chapter we define, develop, and discuss Edgeworth expansions as approximations to distributions of estimates θ of unknown quantities θ 0. We call θ 0 a “parameter”, for want of a better term. Briefly, if θ is constructed from a sample of size n, and if n 1/2 (θ — θ 0) is asymptotically Normally distributed with zero mean and variance σ 2, then ...
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