Abstract
We propose semiparametric methods to estimate the center and shape of a symmetric population when a representative sample of the population is unavailable due to selection bias. We allow an arbitrary sample selection mechanism determined by the data collection procedure, and we do not impose any parametric form on the population distribution. Under this general framework, we construct a family of consistent estimators of the center that is robust to population model misspecification, and we identify the efficient member that reaches the minimum possible estimation variance. The asymptotic properties and finite sample performance of the estimation and inference procedures are illustrated through theoretical analysis and simulations. A data example is also provided to illustrate the usefulness of the methods in practice.
| Original language | English |
|---|---|
| Pages (from-to) | 1090-1104 |
| Number of pages | 15 |
| Journal | Journal of the American Statistical Association |
| Volume | 108 |
| Issue number | 503 |
| DOIs | |
| State | Published - 2013 |
Bibliographical note
Funding Information:Yanyuan Ma, Department of Statistics, Texas A&M University, College Station, TX 77843-3143 (E-mail: [email protected]). Mijeong Kim, Department of Statistics, Texas A&M University, College Station, TX 77843-3143 (E-mail: [email protected]). Marc G. Genton is Professor, CEMSE Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia (E-mail: [email protected]). This research was partially supported by NSF grants DMS-0906341, DMS-1007504, and DMS-1100492; NINDS grant R01-NS073671; and by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
Keywords
- Efficiency
- Nonrandom data
- Robustness
- Semiparametric model
- Skewness
- Symmetric distribution