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How to Select Representative Samples
Department of Forest Resource Management, Swedish University of Agricultural Sciences, Umeå, Sweden.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2014 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 41, no 2, 277-290 p.Article in journal (Refereed) Published
Abstract [en]

We give a formal definition of a representative sample, but roughly speaking, it is a scaled-down version of the population, capturing its characteristics. New methods for selecting representative probability samples in the presence of auxiliary variables are introduced. Representative samples are needed for multipurpose surveys, when several target variables are of interest. Such samples also enable estimation of parameters in subspaces and improved estimation of target variable distributions. We describe how two recently proposed sampling designs can be used to produce representative samples. Both designs use distance between population units when producing a sample. We propose a distance function that can calculate distances between units in general auxiliary spaces. We also propose a variance estimator for the commonly used Horvitz–Thompson estimator. Real data as well as illustrative examples show that representative samples are obtained and that the variance of the Horvitz–Thompson estimator is reduced compared with simple random sampling.

Place, publisher, year, edition, pages
2014. Vol. 41, no 2, 277-290 p.
Keyword [en]
auxiliary variables, local pivotal method, spatially correlated Poisson sampling
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-53279DOI: 10.1111/sjos.12016ISI: 000335388400001OAI: oai:DiVA.org:umu-53279DiVA: diva2:511110
Available from: 2012-03-20 Created: 2012-03-19 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Spatial sampling and prediction
Open this publication in new window or tab >>Spatial sampling and prediction
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis discusses two aspects of spatial statistics: sampling and prediction. In spatial statistics, we observe some phenomena in space. Space is typically of two or three dimensions, but can be of higher dimension. Questions in mind could be; What is the total amount of gold in a gold-mine? How much precipitation could we expect in a specific unobserved location? What is the total tree volume in a forest area? In spatial sampling the aim is to estimate global quantities, such as population totals, based on samples of locations (papers III and IV). In spatial prediction the aim is to estimate local quantities, such as the value at a single unobserved location, with a measure of uncertainty (papers I, II and V).

In papers III and IV, we propose sampling designs for selecting representative probability samples in presence of auxiliary variables. If the phenomena under study have clear trends in the auxiliary space, estimation of population quantities can be improved by using representative samples. Such samples also enable estimation of population quantities in subspaces and are especially needed for multi-purpose surveys, when several target variables are of interest.

In papers I and II, the objective is to construct valid prediction intervals for the value at a new location, given observed data. Prediction intervals typically rely on the kriging predictor having a Gaussian distribution. In paper I, we show that the distribution of the kriging predictor can be far from Gaussian, even asymptotically. This motivated us to propose a semiparametric method that does not require distributional assumptions. Prediction intervals are constructed from the plug-in ordinary kriging predictor. In paper V, we consider prediction in the presence of left-censoring, where observations falling below a minimum detection limit are not fully recorded. We review existing methods and propose a semi-naive method. The semi-naive method is compared to one model-based method and two naive methods, all based on variants of the kriging predictor.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2012. 42 p.
Keyword
Auxiliary variables, Censoring, Inclusion probabilities, Kriging, Local pivotal method, Minimum detection limit, Prediction intervals, Representative sample, Spatial process, Spatial sampling, Semiparametric bootstrap
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-53286 (URN)978-91-7459-373-0 (ISBN)
Public defence
2012-04-12, MIT-huset, MA 121, Umeå universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2012-03-22 Created: 2012-03-20 Last updated: 2012-03-20Bibliographically approved

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