TY - JOUR
T1 - Locally efficient semiparametric estimators for generalized skew-elliptical distributions
AU - Ma, Yanyuan
AU - Genton, Marc G.
AU - Tsiatis, Anastasios A.
N1 - Funding Information:
Yanyuan Ma is Assistant Professor, Department of Statistics, Texas A&M University, College Station, TX 77843 (E-mail: [email protected]). Marc G. Genton is Associate Professor, Department of Statistics, Texas A&M University, College Station, TX 77843 (E-mail: [email protected]). Anastasios A. Tsiatis is Professor, Department of Statistics, North Carolina State University, Box 8203, Raleigh, NC 27695 (E-mail: [email protected]). The work of Yanyuan Ma is supported by grant NIGMS 1 R01 Gm67299-01. The authors thank the editor, the associate editor, and three referees for helpful comments that greatly improved the manuscript.
PY - 2005/9
Y1 - 2005/9
N2 - We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model. We show that these estimators are consistent and asymptotically normal. We present the semiparametric efficiency bound and derive the locally efficient estimator that achieves this bound if the model for the skewing function is correctly specified. The estimators that we propose are consistent and asymptotically normal even if the model for the skewing function is misspecified, and we compute the loss of efficiency in such cases. We conduct a simulation study and provide an illustrative example. Our method is applicable to generalized skew-elliptical distributions.
AB - We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model. We show that these estimators are consistent and asymptotically normal. We present the semiparametric efficiency bound and derive the locally efficient estimator that achieves this bound if the model for the skewing function is correctly specified. The estimators that we propose are consistent and asymptotically normal even if the model for the skewing function is misspecified, and we compute the loss of efficiency in such cases. We conduct a simulation study and provide an illustrative example. Our method is applicable to generalized skew-elliptical distributions.
UR - http://www.scopus.com/inward/record.url?scp=19744376609&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=19744376609&partnerID=8YFLogxK
U2 - 10.1198/016214505000000079
DO - 10.1198/016214505000000079
M3 - Review article
AN - SCOPUS:19744376609
SN - 0162-1459
VL - 100
SP - 980
EP - 989
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 471
ER -