HorvitzThompsonEstimator
The Horvitz–Thompson estimator, named after Daniel N. Horvitz and Donovan J. Thompson, is a design-based method used in survey sampling to estimate finite population totals under unequal probability sampling. It was introduced in their 1952 work, A Generalization of Sampling Without Replacement. The estimator is unbiased for the population total when the inclusion probabilities are known and used correctly.
For a finite population U with units i each having a value y_i and inclusion probability π_i,
Variance and variance estimation: The design-based variance of hat T_HT is Var(hat T_HT) = sum_i sum_j (π_ij
Applications and limitations: The Horvitz–Thompson estimator is widely used in official statistics and health and social