Small area estimators based on restricted mixed models
Tóm tắt
This paper proposes a new model-based approach to estimate small areas that extends the Fay–Herriot methodology. The new model is additive, with a random term to characterize the inter-area variability and a nonparametric mean function specification, defined using the information on an auxiliary variable. The most significant advantage of the proposal is that it avoids the model misspecification problem. The monotonicity is the only assumption about the functional form of the relationship between the variable of interest and the auxiliary one. Estimators for the area means are derived combining “Order Restricted Inference” and standard mixed model approaches. A large simulation experiment shows how the new approach outperforms the Fay–Herriot methodology in many scenarios. Besides, the new method is applied to the Australian farms data.
Tài liệu tham khảo
citation_journal_title=Biometrika; citation_title=M-quantile models for small area estimation; citation_author=R Chambers, N Tzavidis; citation_volume=93; citation_issue=2; citation_publication_date=2006; citation_pages=255-268; citation_doi=10.1093/biomet/93.2.255; citation_id=CR1
citation_journal_title=Ann Stat; citation_title=Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models; citation_author=S Chatterjee, P Lahiri, H Li; citation_volume=36; citation_issue=3; citation_publication_date=2008; citation_pages=1221-1245; citation_doi=10.1214/07-AOS512; citation_id=CR2
David B (2003) Choosing a method for poverty mapping. Food and Agriculture Organization of the United Nations, Rome
citation_journal_title=J Am Stat Assoc; citation_title=Data analysis using Stein’s estimator and its generalizations; citation_author=B Efron, CN Morris; citation_volume=70; citation_publication_date=1975; citation_pages=311-319; citation_doi=10.2307/2285814; citation_id=CR4
citation_journal_title=J Am Stat Assoc; citation_title=Estimates of income for small places: an application of James–Stein procedures to census data; citation_author=RE Fay, RA Herriot; citation_volume=74; citation_publication_date=1979; citation_pages=341-353; citation_id=CR5
citation_journal_title=J Stat Comput Simul; citation_title=Bootstrap mean squared error of a small-area EBLUP; citation_author=W González-Manteiga, MJ Lombardía, I Molina, D Morales, L Santamaría; citation_volume=78; citation_issue=5; citation_publication_date=2008; citation_pages=443-462; citation_doi=10.1080/00949650601141811; citation_id=CR6
citation_journal_title=J R Stat Soc, Ser B; citation_title=On parametric bootstrap methods for small area prediction; citation_author=P Hall, T Maiti; citation_volume=68; citation_issue=2; citation_publication_date=2006; citation_pages=221-238; citation_doi=10.1111/j.1467-9868.2006.00541.x; citation_id=CR7
Huang ET, Bell W (2006) Using the t-distribution in small area estimation: an application to SAIPE state poverty models. SAIPE publications. US Census Bureau
Mammen E, Yu K (2007) Additive isotonic regression. Lecture notes monograph series, vol 55, pp 179–195
citation_journal_title=J R Stat Soc B; citation_title=Non-parametric small area estimation using penalized spline regression; citation_author=J Opsomer, G Claeskens, M Ranalli, G Kauermann, FJ Breidt; citation_volume=70; citation_issue=1; citation_publication_date=2008; citation_pages=265-286; citation_doi=10.1111/j.1467-9868.2007.00635.x; citation_id=CR10
citation_journal_title=J Stat Plan Inference; citation_title=On estimation and testing arising from order restricted balanced mixed models; citation_author=G Pan, R Khattree; citation_volume=77; citation_publication_date=1999; citation_pages=281-292; citation_doi=10.1016/S0378-3758(98)00191-8; citation_id=CR11
citation_title=Small area estimation; citation_publication_date=2003; citation_id=CR12; citation_author=JNK Rao; citation_publisher=Wiley
citation_title=Order restricted statistical inference; citation_publication_date=1988; citation_id=CR13; citation_author=T Robertson; citation_author=FT Wright; citation_author=RL Dykstra; citation_publisher=Wiley
citation_journal_title=Stat Transit J; citation_title=A restricted model approach to improve the precision of estimators; citation_author=C Rueda, JA Menéndez; citation_volume=7; citation_issue=3; citation_publication_date=2005; citation_pages=697; citation_id=CR14
citation_title=Constrained statistical inference; citation_publication_date=2005; citation_id=CR15; citation_author=MJ Silvapulle; citation_author=PK Sen; citation_publisher=Wiley
citation_journal_title=Comput Stat Data Anal; citation_title=Spline smoothing in small area trend estimation and forecasting; citation_author=MD Ugarte, T Goicoa, AF Militino, M Durbán; citation_volume=53; citation_publication_date=2009; citation_pages=3616-3629; citation_doi=10.1016/j.csda.2009.02.027; citation_id=CR16
citation_journal_title=Test; citation_title=Benchmarked estimators in small areas using linear mixed models with restrictions; citation_author=MD Ugarte, AF Militino, T Goicoa; citation_volume=18; citation_issue=2; citation_publication_date=2009; citation_pages=342-364; citation_doi=10.1007/s11749-008-0094-x; citation_id=CR17