Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling

Myoung Jae Lee, Sanghyeok Lee

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationMissing Data Methods
Subtitle of host publicationCross-Sectional Methods and Applications
EditorsWilliam Greene, David Drukker
Number of pages29
Publication statusPublished - 2011

Publication series

NameAdvances in Econometrics
Volume27 A
ISSN (Print)0731-9053


  • Choicebased sampling
  • Endogenous sampling
  • Standard stratified sampling
  • Truncated regression

ASJC Scopus subject areas

  • Economics and Econometrics


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