Hierarchical weighted least squares in the presence of missing data

Sergey S. Tarima, Yuriy G. Dmitriev, Richard J. Kryscio

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper derives two classes of minimum variance estimators in the presence of missing data. One estimator represents an alternative expression to Weighted Least Square (WLS). Another estimator, hierarchical WLS or HWLS is identical to WLS for normal and categorical missing data. However, WLS and HWLS are different in general and this manuscript focuses on this new class of estimators. Application of HWLS to random dropout survival data yields the well-known Kaplan-Meier estimator. Simulation studies compare WLS, HWLS, and Expectation Maximization (EM) for the difference in means in a bivariate normal model. Another set of simulations compares WLS, HWLS, and Multiple Imputation (MI) under normality assumption for the difference in medians in a bivariate exponential model. Both Missing Completely At Random (MCAR) and Missing At Random (MAR) data are considered in these simulation studies. Finally, HWLS is applied to estimating parameters of a proportional hazards model in a well known mouse leukemia dataset with missing covariates.

Original languageEnglish
Pages (from-to)125-136
Number of pages12
JournalModel Assisted Statistics and Applications
Issue number3
StatePublished - 2007


  • Hierarchical structures
  • Missing and censored data
  • Parameter estimation
  • Weighted least squares

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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