Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Comparing two samples by penalized logistic regression
AU - Fokianos, K.
PY - 2008
Y1 - 2008
N2 - Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log–likelihood function of two unknown densities is of some parametric form. The model has been extended to cover multiple samples problems while its theoretical properties have been investigated using large sample theory. A main application of the density ratio model is testing whether two, or more, distributions are equal. We extend these results by arguing that the penalized maximum empirical likelihood estimator has less mean square error than that of the ordinary maximum likelihood estimator, especially for small samples. In fact, penalization resolves any existence problems of estimators and a modified Wald type test statistic can be employed for testing equality of the two distributions. A limited simulation study supports further the theory.
AB - Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log–likelihood function of two unknown densities is of some parametric form. The model has been extended to cover multiple samples problems while its theoretical properties have been investigated using large sample theory. A main application of the density ratio model is testing whether two, or more, distributions are equal. We extend these results by arguing that the penalized maximum empirical likelihood estimator has less mean square error than that of the ordinary maximum likelihood estimator, especially for small samples. In fact, penalization resolves any existence problems of estimators and a modified Wald type test statistic can be employed for testing equality of the two distributions. A limited simulation study supports further the theory.
KW - Empirical likelihood
KW - biased sampling
KW - penalty
KW - semiparametric
KW - shrinkage
KW - mean square error
KW - power
U2 - 10.1214/07-EJS078
DO - 10.1214/07-EJS078
M3 - Journal article
VL - 2
SP - 564
EP - 580
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
ER -