Two-phase rejective sampling and its asymptotic properties

Area of Science:

• Statistics
• Survey Methodology
• Finite Population Sampling

Background:

• Rejective sampling is efficient for single-phase surveys with auxiliary information.
• Auxiliary information is often unavailable in practical survey designs.
• Existing single-phase rejective sampling lacks fully established asymptotic theory.

Purpose of the Study:

• To introduce and analyze two-phase rejective sampling (TPRS) for situations lacking auxiliary information.
• To investigate the asymptotic design properties of estimators under TPRS.
• To extend TPRS to accommodate varying covariate importance and multi-phase sampling.

Main Methods:

• Developed a two-phase sampling framework incorporating rejective sampling in the second phase.
• Explored asymptotic properties of double expansion and regression estimators under TPRS.
• Extended theoretical framework to general estimating equations and multi-phase designs.

Main Results:

• TPRS significantly enhances the efficiency of the double-expansion estimator.
• The TPRS-enhanced double-expansion estimator achieves efficiency comparable to regression estimators.
• Asymptotic results for TPRS encompass and clarify single-phase rejective sampling theory.

Conclusions:

• TPRS offers a robust and efficient alternative for surveys when auxiliary information is absent.
• The proposed method provides theoretical advancements for rejective sampling techniques.
• TPRS is extendable to complex survey designs, including multi-phase sampling and varying covariate importance.