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Two-phase rejective sampling and its asymptotic properties.

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Two-phase rejective sampling (TPRS) enhances survey efficiency when auxiliary information is unavailable. This method improves the double expansion estimator, making it competitive with regression estimators in finite population sampling.

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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.