In statistics, the Horvitz–Thompson estimator, named after Daniel G. Horvitz and Donovan J. Thompson,[1] is a method for estimating the total[2] and mean of a pseudo-population in a stratified sample by applying inverse probability weighting to account for the difference in the sampling distribution between the collected data and the target population.
The Horvitz–Thompson estimator is frequently applied in survey analyses and can be used to account for missing data, as well as many sources of unequal selection probabilities.
be an independent sample from n of N ≥ n distinct strata with a common mean μ.
is the inclusion probability that a randomly sampled individual in a superpopulation belongs to the ith stratum.
is considered the proportion of individuals in a target population belonging to the ith stratum.
could be thought of as an estimate of the complete sample of persons within the ith stratum.
It can also be viewed as a special case of multiple imputation approaches.
[5] The "survey" package for R conducts analyses for post-stratified data using the Horvitz–Thompson estimator.
, as follows: The Hansen–Hurwitz (1943) is known to be inferior to the Horvitz–Thompson (1952) strategy, associated with a number of Inclusion Probabilities Proportional to Size (IPPS) sampling procedures.