In survey sampling theory, a finite population of fixed but unknown values is sampled with unequal, known inclusion probabilities for each unit; the Horvitz–Thompson estimator constructs an unbiased estimate of the population total (or mean) by weighting each sampled observation by the inverse of its inclusion probability, a technique also known as inverse probability weighting. The estimator's unbiasedness follows directly from rewriting the sum using indicator random variables over the entire population and applying linearity of expectation, but unbiasedness alone does not guarantee that an estimator is statistically sensible, since inverse-probability weighting can produce estimates with extremely poor precision when inclusion probabilities are highly unequal, illustrating the broader distinction between bias and other criteria for evaluating estimators in statistical inference.
In survey sampling theory, a finite population of fixed but unknown values is sampled with unequal, known inclusion probabilities for each unit; the Horvitz–Thompson estimator constructs an unbiased …