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Higher‐order approximations for pitman estimators and for optimal compromise estimators
Author(s) -
Ventura Laura
Publication year - 1998
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 - 10.2307/3315672
Subject(s) - estimator , mathematics , laplace's method , laplace transform , monte carlo method , m estimator , compromise , scale (ratio) , function (biology) , maximum likelihood , mathematical optimization , statistics , mathematical analysis , physics , social science , quantum mechanics , evolutionary biology , sociology , biology
Laplace approximations for the Pitman estimators of location or scale parameters, including terms O ( n −1 ), are obtained. The resulting expressions involve the maximum‐likelihood estimate and the derivatives of the log‐likelihood function up to order 3. The results can be used to refine the approximations for the optimal compromise estimators for location parameters considered by Easton (1991). Some applications and Monte Carlo simulations are discussed.