3.3 The Horvitz-Thompson Estimator STAT 506 - Sampling Theory and Methods

# 3.3 The Horvitz-Thompson Estimator STAT 506 - Sampling Theory and Methods

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ANGEL Department of Statistics Eberly College of Science Home // Lesson 3: Unequal Probability Sampling 3.3 The Horvitz-Thompson Estimator Submitted by gfj100 on Tue, 12/01/2009 - 09:40 Unit Summary Horvitz-Thompson Estimator (any design) To compute the variance of the Horvitz-Thompson estimators Any Design: The Horvitz-Thompson Estimator Horvitz-Thompson (1952) introduced an unbiased estimator for τ for any design, with or without replacement. Definition: π i , i = 1, . .. , N are given positive numbers that represent the probability that unit i is included in the sample under a given sampling scheme. The Horvitz-Thompson estimator is: Where ν is the distinct number of units in the sample. The Horvitz-Thompson estimator does not depend on the number of times a unit may be selected. Each distinct unit of the sample is utilized only once. Read section 6.5 in the text. The section reviews the proofs for how the following two formula are derived.

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## This note was uploaded on 09/10/2010 for the course STAT 506 at Pennsylvania State University, University Park.

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3.3 The Horvitz-Thompson Estimator STAT 506 - Sampling Theory and Methods

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