TY - CHAP
T1 - Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling
AU - Lee, Myoung Jae
AU - Lee, Sanghyeok
PY - 2011
Y1 - 2011
N2 - Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y ('endogenous samples') or if some Y-dependent strata are not sampled at all ('truncated sample' - A missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator 'Estimated- EX MLE' is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of 'Fixed-X MLE' which conditions on X, even if the extra sample size is small. In fact, Estimated-EXMLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the 'Known-F XMLE'. A small-scale simulation study is provided to illustrate these points.
AB - Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y ('endogenous samples') or if some Y-dependent strata are not sampled at all ('truncated sample' - A missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator 'Estimated- EX MLE' is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of 'Fixed-X MLE' which conditions on X, even if the extra sample size is small. In fact, Estimated-EXMLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the 'Known-F XMLE'. A small-scale simulation study is provided to illustrate these points.
KW - Choicebased sampling
KW - Endogenous sampling
KW - Standard stratified sampling
KW - Truncated regression
UR - http://www.scopus.com/inward/record.url?scp=84869156377&partnerID=8YFLogxK
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U2 - 10.1108/S0731-9053(2011)000027A006
DO - 10.1108/S0731-9053(2011)000027A006
M3 - Chapter
AN - SCOPUS:84869156377
SN - 9781780525242
T3 - Advances in Econometrics
SP - 63
EP - 91
BT - Missing Data Methods
A2 - Greene, William
A2 - Drukker, David
ER -