Abstract
In simple random sampling without replacement (SRSWOR), certain reverse martingale structures render simple asymptotics for the conventional linear statistics. In unequal probability sampling (UPS) WOR, such martingale-based methodology may not be generally adoptable. General asymptotics for UPSWOR sampling schemes, developed by Hartley and Rao (Ann. Math. Statist. 33 (1962) 350), and Hájek (Ann. Math. Statist. 35 (1964) 1491), rest on different sets of regularity assumptions, and they differ in their treatise too. Some anomalies in this context are eliminated here with a reconciliation of both the approaches, and estimation of the asymptotic variance of linear estimators is considered in the same vein. Applications to small area sampling are also stressed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 71-81 |
| Number of pages | 11 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 102 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 1 2002 |
Keywords
- Finite population correction
- Horvitz-Thompson estimator
- Inclusion probabilities
- Poisson sampling scheme
- Rejective sampling
- SRSWOR
- SRSWR
- Successive sampling
- Variance estimators
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics