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Approximate and estimated saddlepoint approximations
Author(s) -
OhmanStrickland Pamela,
Casella George
Publication year - 2002
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 - 10.2307/3315867
Subject(s) - cumulant , approximations of π , mathematics , edgeworth series , function (biology) , distribution (mathematics) , approximation error , order (exchange) , statistics , mathematical analysis , finance , evolutionary biology , economics , biology
Classical saddlepoint methods, which assume that the cumulant generating function is known, result in an approximation to the distribution that achieves an error of order O ( n −1 ). The authors give a general theorem to address the accuracy of saddlepoint approximations in which the cumulant generating function has been estimated or approximated. In practice, the resulting saddlepoint approximations are typically of the order O ( n −1/2 ). The authors give simulation results for small sample examples to compare estimated saddlepoint approximations.