Characterization of the Consistent Weighted Regression Estimators.
Abstract
The ratio estimator can be justified by a linear superpopulation model without intercept and the error variance proportional to the size of the covariate. If either of the assumptions is violated, then other estimators may be considered. We study the consistency of several estimators which are based on different assumptions about variance structure of the error. Some decompositions of the finite population are introduced. Roughly speaking, we fit a weighted regression line to the finite population with the weight chosen according to the estimator under consideration. We show that any estimators in that class, except the ratio estimator, are inconsistent unless some conditions on the population's characteristics are satisfied. Based on the decomposition, modifications can be made to get a consistent estimator. For the case of p-auxiliary variables, we characterize the class of consistent weighted least squares estimators. The result is extended to the infinite population problem using a completely different approach.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1985
- Accession Number
- ADA163605
Entities
People
- Lih-yuan Deng
Organizations
- University of Wisconsin–Madison