Abstract
In the previous chapter we have seen how useful the sampling autocorrelation coefficient ρ z is for deriving formulas for variance estimators in case of unequal probability sampling from a finite population. Especially in case of sampling with replacement, the formulas are straightforward because ρ z = 0 or, equivalently, the sample observations are uncorrelated for such sampling designs. This applies to multistage sampling designs as well. From a geometric point of view this means that the random variables z i are mutually orthogonal (i = 1,...,n). In this chapter we will give a more detailed geometric interpretation of ρ z in case of unequal probability sampling without replacement. Before doing this we give a comprehensive and a somewhat more formal description of the alternative rho approach to unequal probability sampling. In the next section we first pay attention to the classical Horvitz-Thompson estimator (for short, the HT estimator).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Knottnerus, P. (2003). A General Rho Theory on Survey Sampling. In: Sample Survey Theory. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21764-2_4
Download citation
DOI: https://doi.org/10.1007/978-0-387-21764-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2988-4
Online ISBN: 978-0-387-21764-2
eBook Packages: Springer Book Archive