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On Methods for Real Time Sampling and Distributions in Sampling
Umeå University, Faculty of Science and Technology, Mathematical statistics.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

This thesis is composed of six papers, all dealing with the issue of sampling from a finite population. We consider two different topics: real time sampling and distributions in sampling. The main focus is on Papers A–C, where a somewhat special sampling situation referred to as real time sampling is studied. Here a finite population passes or is passed by the sampler. There is no list of the population units available and for every unit the sampler should decide whether or not to sample it when he/she meets the unit. We focus on the problem of finding suitable sampling methods for the described situation and some new methods are proposed. In all, we try not to sample units close to each other so often, i.e. we sample with negative dependencies. Here the correlations between the inclusion indicators, called sampling correlations, play an important role. Some evaluation of the new methods are made by using a simulation study and asymptotic calculations. We study new methods mainly in comparison to standard Bernoulli sampling while having the sample mean as an estimator for the population mean. Assuming a stationary population model with decreasing autocorrelations, we have found the form for the nearly optimal sampling correlations by using asymptotic calculations. Here some restrictions on the sampling correlations are used. We gain most in efficiency using methods that give negatively correlated indicator variables, such that the correlation sum is small and the sampling correlations are equal for units up to lag m apart and zero afterwards. Since the proposed methods are based on sequences of dependent Bernoulli variables, an important part of the study is devoted to the problem of how to generate such sequences. The correlation structure of these sequences is also studied.

The remainder of the thesis consists of three diverse papers, Papers D–F, where distributional properties in survey sampling are considered. In Paper D the concern is with unified statistical inference. Here both the model for the population and the sampling design are taken into account when considering the properties of an estimator. In this paper the framework of the sampling design as a multivariate distribution is used to outline two-phase sampling. In Paper E, we give probability functions for different sampling designs such as conditional Poisson, Sampford and Pareto designs. Methods to sample by using the probability function of a sampling design are discussed. Paper F focuses on the design-based distributional characteristics of the π-estimator and its variance estimator. We give formulae for the higher-order moments and cumulants of the π-estimator. Formulae of the design-based variance of the variance estimator, and covariance of the π-estimator and its variance estimator are presented.

##### Place, publisher, year, edition, pages
Umeå: Matematisk statistik , 2004. , p. 162
##### Keyword [en]
Mathematical statistics, Finite population sampling, inferential issues, real time sampling, sequential sampling methods, negative sampling correlations, model-design-based inference, multivariate Bernoulli and multinomial designs
##### Keyword [sv]
Matematisk statistik
##### National Category
Probability Theory and Statistics
##### Research subject
Mathematical Statistics
##### Identifiers
ISBN: 91-7305-795-9 (print)OAI: oai:DiVA.org:umu-415DiVA, id: diva2:143404
##### Public defence
2005-02-04, MA121, MIT-huset, Umeå universitet, Umeå, 13:00 (English)
##### Opponent
Available from: 2005-01-13 Created: 2005-01-13 Last updated: 2010-01-29Bibliographically approved
##### List of papers
1. Some real time sampling methods
Open this publication in new window or tab >>Some real time sampling methods
##### Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2001. p. 23
##### Series
Research report / Department of Mathematical Statistics, Umeå University, ISSN 1401-730X ; 2001:02
##### National Category
Probability Theory and Statistics
##### Identifiers
urn:nbn:se:umu:diva-4348 (URN)
##### Note

Ingår i Kadri Meister's PhD thesis: On Methods for Real Time Sampling and Distributions in Sampling. 2004. ISBN 91-7305-795-9.

Available from: 2005-01-13 Created: 2005-01-13 Last updated: 2014-03-19Bibliographically approved
2. Asymptotic considerations concerning real time sampling methods
Open this publication in new window or tab >>Asymptotic considerations concerning real time sampling methods
2002 In: Statistics in Transition, ISSN 1234-7655, Vol. 5, p. 1037-1050Article in journal (Refereed) Published
##### Identifiers
urn:nbn:se:umu:diva-4349 (URN)
Available from: 2005-01-13 Created: 2005-01-13Bibliographically approved
3. Some different methods to get stationary Bernoulli sequences with negative correlations for sampling applications
Open this publication in new window or tab >>Some different methods to get stationary Bernoulli sequences with negative correlations for sampling applications
##### Identifiers
urn:nbn:se:umu:diva-4350 (URN)
Available from: 2005-01-13 Created: 2005-01-13 Last updated: 2010-01-13Bibliographically approved
4. Statistical inference in sampling theory
Open this publication in new window or tab >>Statistical inference in sampling theory
2001 In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 7, p. 301-316Article in journal (Refereed) Published
##### Identifiers
urn:nbn:se:umu:diva-4351 (URN)
Available from: 2005-01-13 Created: 2005-01-13Bibliographically approved
5. Sampling design and sample selection through distribution theory
Open this publication in new window or tab >>Sampling design and sample selection through distribution theory
2004 (English)In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 123, no 2, p. 395-413Article in journal (Refereed) Published
##### Abstract [en]

This paper may be seen as in part a review covering basics of sampling theory in a different light. We use a multivariate approach with a unifying treatment of WOR and WR sampling designs. In this framework, we present probability functions of several important sampling designs, such as the hypergeometric, the conditional Poisson, the Sampford, and the general order sampling designs among others. Benefiting from the distributional feature of the sampling design, a list-sequential method for generating a sample from any given design is developed. The method is applied to hypergeometric, multinomial, conditional Poisson and Sampford designs. An order sampling procedure for a population with unknown size is described. Markov chain Monte Carlo methods are discussed.

##### Keyword
Multivariate Bernoulli design, Multinomial design, Hypergeometric design, Conditional Poisson design, Sampford design, Order sampling design, List-sequential sampling, Markov chain Monte Carlo, Gibbs sampling
##### National Category
Probability Theory and Statistics
##### Identifiers
urn:nbn:se:umu:diva-7752 (URN)10.1016/S0378-3758(03)00150-2 (DOI)
Available from: 2008-01-11 Created: 2008-01-11 Last updated: 2017-12-14Bibliographically approved
6. On the design-based distribution of some estimators in survey sampling
Open this publication in new window or tab >>On the design-based distribution of some estimators in survey sampling
1997 In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 3, p. 324-329Article in journal (Refereed) Published
##### Identifiers
urn:nbn:se:umu:diva-4353 (URN)
Available from: 2005-01-13 Created: 2005-01-13Bibliographically approved

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Cite
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