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On the Convergence of the Horvitz‐Thompson Estimator
Author(s) -
Robinson P. M.
Publication year - 1982
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1982.tb00829.x
Subject(s) - estimator , statistics , mathematics , consistency (knowledge bases) , convergence (economics) , sampling (signal processing) , mean squared error , population , computer science , discrete mathematics , demography , economics , economic growth , filter (signal processing) , sociology , computer vision
Summary We investigate the degree to which the Horvitz‐Thompson estimator approximates the population mean in survey sampling. Specifically, conditions for (mean square) consistency are given, along with rates of convergence. The conditions involve only first and second‐order inclusion probabilities, and for various sampling designs they are easy to check.