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Saddlepoint approximations for nonlinear statistics
Author(s) -
Wang Soujin
Publication year - 1990
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315456
Subject(s) - statistic , mathematics , simple (philosophy) , nonlinear system , statistics , approximations of π , linear approximation , sample mean and sample covariance , edgeworth series , physics , philosophy , epistemology , quantum mechanics , estimator
It is well known that saddlepoint expansions lead to accurate approximations to the cumulative distributions and densities of a sample mean and other simple linear statistics. The use of such expansions is explored in a broader situation. The saddlepoint formula for the tail probability of a certain type of nonlinear statistic is derived. The relative error of O(n –1 ), as in the linear case, is retained. A simple example is considered, to illustrate the great accuracy of the approximation.