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Entropy of unequal probability sampling designs
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: Statistical Methodology, ISSN 1572-3127, E-ISSN 1878-0954, Vol. 7, no 2, 84-97 p.Article in journal (Refereed) Published
Abstract [en]

There exist many designs for unequal probability sampling. In this paper entropy, which is a measure of randomness, is used to compare eight designs. Both old and commonly used designs and more recent designs are included. Several different and general estimates of entropy are presented. In the quest of finding entropy, expressions for the probability function are derived for different designs. One of them is a recent general design called correlated Poisson sampling. Several designs are close to having maximum entropy, which means that the designs are robust. A few designs yield low entropy and should therefore in general be avoided.

Place, publisher, year, edition, pages
Elsevier Bv. , 2010. Vol. 7, no 2, 84-97 p.
Keyword [en]
Entropy, Probability functions, Sampling designs, Unequal probability sampling
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-31085DOI: 10.1016/j.stamet.2009.10.005OAI: oai:DiVA.org:umu-31085DiVA: diva2:290870
Available from: 2010-01-28 Created: 2010-01-28 Last updated: 2017-12-12Bibliographically approved
In thesis
1. On unequal probability sampling designs
Open this publication in new window or tab >>On unequal probability sampling designs
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The main objective in sampling is to select a sample from a population in order to estimate some unknown population parameter, usually a total or a mean of some interesting variable. When the units in the population do not have the same probability of being included in a sample, it is called unequal probability sampling. The inclusion probabilities are usually chosen to be proportional to some auxiliary variable that is known for all units in the population. When unequal probability sampling is applicable, it generally gives much better estimates than sampling with equal probabilities. This thesis consists of six papers that treat unequal probability sampling from a finite population of units.

A random sample is selected according to some specified random mechanism called the sampling design. For unequal probability sampling there exist many different sampling designs. The choice of sampling design is important since it determines the properties of the estimator that is used. The main focus of this thesis is on evaluating and comparing different designs. Often it is preferable to select samples of a fixed size and hence the focus is on such designs.

It is also important that a design has a simple and efficient implementation in order to be used in practice by statisticians. Some effort has been made to improve the implementation of some designs. In Paper II, two new implementations are presented for the Sampford design.

In general a sampling design should also have a high level of randomization. A measure of the level of randomization is entropy. In Paper IV, eight designs are compared with respect to their entropy. A design called adjusted conditional Poisson has maximum entropy, but it is shown that several other designs are very close in terms of entropy.

A specific situation called real time sampling is treated in Paper III, where a new design called correlated Poisson sampling is evaluated. In real time sampling the units pass the sampler one by one. Since each unit only passes once, the sampler must directly decide for each unit whether or not it should be sampled. The correlated Poisson design is shown to have much better properties than traditional methods such as Poisson sampling and systematic sampling.

Place, publisher, year, edition, pages
Umeå: Department of Mathematics and Mathematical Statistics, Umeå University, 2010. 31 + 6 papers p.
Keyword
conditional Poisson sampling, correlated Poisson sampling, entropy, extended Sampford sampling, Horvitz-Thompson estimator, inclusion probabilities, list-sequential sampling, non-rejective implementation, Pareto sampling, Poisson sampling, probability functions, ratio estimator, real-time sampling, repeated Poisson sampling, Sampford sampling, sampling designs, splitting method, unequal probability sampling
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-33701 (URN)978-91-7264-999-6 (ISBN)
Public defence
2010-05-28, MIT-huset, MA 121, Umeå universitet, Umeå, 13:15 (English)
Opponent
Supervisors
Available from: 2010-05-07 Created: 2010-05-03 Last updated: 2010-05-18Bibliographically approved

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