Final published version
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 - On the effect of misspecifying the density ratio model
AU - Fokianos, K.
AU - Kaimi, I.
PY - 2006/9
Y1 - 2006/9
N2 - The density ratio model specifies that the log-likelihood ratio of two unknown densities is of known linear form which depends on some finite dimensional parameters. The model can be broadened to allow for m-samples in a quite natural way. Estimation of both parametric and nonparametric part of the model is carried out by the method of empirical likelihood. However the assumed linear form has an impact on the estimation and testing for the parametric part. The goal of this study is to quantify the effect of choosing an incorrect linear form and its impact to inference. The issue of misspecification is addressed by embedding the unknown linear form to some parametric transformation family which yields ultimately to its identification. Simulated examples and data analysis integrate the presentation.
AB - The density ratio model specifies that the log-likelihood ratio of two unknown densities is of known linear form which depends on some finite dimensional parameters. The model can be broadened to allow for m-samples in a quite natural way. Estimation of both parametric and nonparametric part of the model is carried out by the method of empirical likelihood. However the assumed linear form has an impact on the estimation and testing for the parametric part. The goal of this study is to quantify the effect of choosing an incorrect linear form and its impact to inference. The issue of misspecification is addressed by embedding the unknown linear form to some parametric transformation family which yields ultimately to its identification. Simulated examples and data analysis integrate the presentation.
KW - Biased sampling
KW - Empirical likelihood
KW - Box–Cox transformation
KW - Mean square error
KW - Bias
KW - Power
U2 - 10.1007/s10463-005-0022-8
DO - 10.1007/s10463-005-0022-8
M3 - Journal article
VL - 58
SP - 475
EP - 497
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
SN - 0020-3157
IS - 3
ER -