TY - JOUR

T1 - Monte Carlo approximation to Edgeworth expansions

AU - Hall, Peter

AU - Martin, Michael A.

AU - Sun, Shan

PY - 1999/9

Y1 - 1999/9

N2 - Since the 1930s, empirical Edgeworth expansions have been employed to develop techniques for approximate, nonparametric statistical inference. The introduction of bootstrap methods has increased the potential usefulness of Edgeworth approximations. In particular, a recent paper by Lee & Young introduced a novel approach to approximating bootstrap distribution functions, using first an empirical Edgeworth expansion and then a more traditional bootstrap approximation to the remainder. In principle, either direct calculation or computer algebra could be used to compute the Edgeworth component, but both methods would often be difficult to implement in practice, not least because of the sheer algebraic complexity of a general Edgeworth expansion. In the present paper we show that a simple but nonstandard Monte Carlo technique is a competitive alternative. It exploits properties of Edgeworth expansions, in particular their parity and the degrees of their polynomial terms, to develop particularly accurate approximations.

AB - Since the 1930s, empirical Edgeworth expansions have been employed to develop techniques for approximate, nonparametric statistical inference. The introduction of bootstrap methods has increased the potential usefulness of Edgeworth approximations. In particular, a recent paper by Lee & Young introduced a novel approach to approximating bootstrap distribution functions, using first an empirical Edgeworth expansion and then a more traditional bootstrap approximation to the remainder. In principle, either direct calculation or computer algebra could be used to compute the Edgeworth component, but both methods would often be difficult to implement in practice, not least because of the sheer algebraic complexity of a general Edgeworth expansion. In the present paper we show that a simple but nonstandard Monte Carlo technique is a competitive alternative. It exploits properties of Edgeworth expansions, in particular their parity and the degrees of their polynomial terms, to develop particularly accurate approximations.

KW - Bootstrap

KW - Edgeworth approximation

KW - Edgeworth expansions

KW - Least squares

KW - Monte Carlo approximation

KW - Monte Carlo methods

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=0033260539&partnerID=8YFLogxK

U2 - 10.2307/3316113

DO - 10.2307/3316113

M3 - Article

SN - 0319-5724

VL - 27

SP - 579

EP - 584

JO - Canadian Journal of Statistics

JF - Canadian Journal of Statistics

IS - 3

ER -