Petersen estimator, Chapman adjustment, list effects, and heterogeneity

Area of Science:

• Statistics
• Population Estimation
• Nonparametric Methods

Background:

• Estimating population size from multiple incomplete lists is challenging.
• Existing methods often struggle with varying individual and list effects.

Purpose of the Study:

• To develop a nonparametric mixture model for population size estimation from multiple lists.
• To propose an analytically expressed lower bound for population size.
• To assess the performance of the proposed methods through simulations and real-world applications.

Main Methods:

• A nonparametric mixture model is utilized to accommodate varying individual and list effects.
• A lower bound for population size with an analytic expression is derived.
• Asymptotic normality of the proposed estimator is established.
• Adjusted versions of the estimator and its variance bound are developed.

Main Results:

• An analytically expressed lower bound for population size is proposed.
• The lower bound can be estimated without complex model-fitting.
• The adjusted estimator and variance bound are shown to be unbiased in the limit.
• Simulation experiments and real applications demonstrate the approach's utility.

Conclusions:

• The proposed nonparametric mixture model offers a robust method for population size estimation.
• The novel lower bound provides a valuable tool for assessing population size estimates.
• The adjusted estimators ensure reliable and unbiased results in the long run.