Empirical likelihood in the presence of nuisance parameters Export

@article{lazar:mykland:1999, abstract = {Empirical likelihood was introduced as a nonparametric analogue of ordinary parametric likelihood. It is well known that the empirical likelihood ratio statistic inherits a number of properties of the parametric likelihood ratio statistic, such as the aymptotic chi-squared distribution and Bartlett correctability. This raises the question of whether or not the same is true in the presence of nuisance parameters. Recent work by Qin Lawless (1994) indicates that the chi-squared distribution is still valid to first order. We show that, when nuisance parameters are present, as introduced via a system of estimating equations, the asymptotic expansion for the signed square root of the empirical likelihood ratio statistic has a nonstandard form. This implies that the empirical likelihood ratio statistic itself does not permit a Bartlett correction. Keywords:Accuracy; Bartlett correction; Edgeworth expansion; Empirical likelihood; General estimating equation; Likelihood inference; Likelihood ratio test; Martingale inference. 10.1093/biomet/86.1.203}, author = {Lazar, N. A. and Mykland, P. A.}, citeulike-article-id = {5098910}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/biomet/86.1.203}, citeulike-linkout-1 = {http://biomet.oxfordjournals.org/cgi/content/abstract/86/1/203}, day = {1}, doi = {10.1093/biomet/86.1.203}, journal = {Biometrika}, keywords = {asymptotics, empirical\_likelihood}, month = {March}, number = {1}, pages = {203--211}, posted-at = {2009-07-09 21:31:01}, priority = {2}, title = {Empirical likelihood in the presence of nuisance parameters}, url = {http://dx.doi.org/10.1093/biomet/86.1.203}, volume = {86}, year = {1999} }

TY - JOUR ID - lazar:mykland:1999 L3 - citeulike-article-id:5098910 N2 - Empirical likelihood was introduced as a nonparametric analogue of ordinary parametric likelihood. It is well known that the empirical likelihood ratio statistic inherits a number of properties of the parametric likelihood ratio statistic, such as the aymptotic chi-squared distribution and Bartlett correctability. This raises the question of whether or not the same is true in the presence of nuisance parameters. Recent work by Qin Lawless (1994) indicates that the chi-squared distribution is still valid to first order. We show that, when nuisance parameters are present, as introduced via a system of estimating equations, the asymptotic expansion for the signed square root of the empirical likelihood ratio statistic has a nonstandard form. This implies that the empirical likelihood ratio statistic itself does not permit a Bartlett correction. Keywords:Accuracy; Bartlett correction; Edgeworth expansion; Empirical likelihood; General estimating equation; Likelihood inference; Likelihood ratio test; Martingale inference. 10.1093/biomet/86.1.203 IS - 1 JF - Biometrika EP - 211 TI - Empirical likelihood in the presence of nuisance parameters VL - 86 SP - 203 KW - asymptotics KW - empirical_likelihood AU - Lazar, NA AU - Mykland, PA PY - 1999/03/01/ UR - http://dx.doi.org/10.1093/biomet/86.1.203 ER -