Edgeworth Expansions and Smoothness

Rearranging Edgeworth- Cornish-Fisher Expansions

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of distribution and quantile functions, the procedure often delivers strikingly better approximations to the dist...

Interpretation and Manipulation of Edgeworth Expansions

Edgeworth Expansions for Errors-in-Variables Models

Edgeworth expansions for sums of independent but not identically distributed multivariate random vectors are established. The results are applied to get valid Edgeworth expansions for estimates of regression parameters in linear errors-invariable models. The expansions for studentized versions are also developed. Further, Edgeworth expansions for the corresponding bootstrapped statistics are ob...

Approximating random inequalities with Edgeworth expansions

Random inequalities of the form

Tilted Edgeworth Expansions for Asymptotically Normal Vectors

We obtain the Edgeworth expansion for P (n1/2(θ̂− θ) < x) and its derivatives, and the tilted Edgeworth (or saddlepoint or small sample) expansion for P (θ̂ < x) and its derivatives where θ̂ is any vector estimate having the standard cumulant expansions in powers of n−1. AMS 2000 Subject Classification: Primary 60F10; Secondary 62F05.