Sampling Designs with Linear and Quadratic Probability Functions
Affiliation(s)
Department of Mathematics and Mathematical Statistics, Ume? University, Ume?, Sweden . Department of Forest Resource Management, Swedish University of Agricultural Sciences, Ume?, Sweden . Institute of Mathematical Statistics, University of Tartu, Tartu, Estonia.
Department of Mathematics and Mathematical Statistics, Ume? University, Ume?, Sweden . Department of Forest Resource Management, Swedish University of Agricultural Sciences, Ume?, Sweden . Institute of Mathematical Statistics, University of Tartu, Tartu, Estonia.
ABSTRACT
Fixed size without replacement sampling designs with probability functions that are linear or quadratic functions of the sampling indicators are defined and studied. Generality, simplicity, remarkable properties, and also somewhat restricted flexibility characterize these designs. It is shown that the families of linear and quadratic designs are closed with respect to sample complements and with respect to conditioning on sampling outcomes for specific units. Relations between inclusion probabilities and parameters of the probability functions are derived and sampling procedures are given.
Cite this paper
Bondesson, L. , Grafström, A. and Traat, I. (2014) Sampling Designs with Linear and Quadratic Probability Functions. Open Journal of Statistics, 4, 178-187. doi: 10.4236/ojs.2014.43017.
Bondesson, L. , Grafström, A. and Traat, I. (2014) Sampling Designs with Linear and Quadratic Probability Functions. Open Journal of Statistics, 4, 178-187. doi: 10.4236/ojs.2014.43017.
References
[1] Midzuno, H. (1952) On the Sampling System with Probability Proportional to Sum of Sizes. Annals of the Institute of Statistical Mathematics, 3, 99-107. http://dx.doi.org/10.1007/BF02949779 [2] Bondesson, L. and Traat, I. (2013) On Sampling Designs with Ordered Conditional Inclusion Probabilities. Scandinavian Journal of Statistics, 40, 724-733. http://dx.doi.org/10.1111/sjos.12024 [3] Sinha, B.K. (1973) On Sampling Schemes to Realize Preassigned Sets of Inclusion Probabilities of First Two Orders. Calcutta Statistical Association Bulletin, 22, 89-110. [4] Tillé, Y. (2006) Sampling Algorithms. Springer, New York. [5] Brewer, K.R.W. and Hanif, M. (1983) Sampling with Unequal Probabilities. Lecture Notes in Statistics, No. 15, Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4684-9407-5 [6] Wywial, J. (2000) On Precision of Horvitz-Thompson Strategies. Statistics in Transition, 4, 779-798. [7] Bondesson, L., Traat, I. and Lundqvist, A. (2006) Pareto Sampling versus Conditional Poisson and Sampford Sampling. Scandinavian Journal of Statistics, 33, 699-720.
http://dx.doi.org/10.1111/j.1467-9469.2006.00497.x [8] Bondesson, L. (2012) On Sampling with Prescribed Second-Order Inclusion Probabilities. Scandinavian Journal of Statistics, 39, 813-829. http://dx.doi.org/10.1111/j.1467-9469.2012.00808.x
[1] Midzuno, H. (1952) On the Sampling System with Probability Proportional to Sum of Sizes. Annals of the Institute of Statistical Mathematics, 3, 99-107. http://dx.doi.org/10.1007/BF02949779 [2] Bondesson, L. and Traat, I. (2013) On Sampling Designs with Ordered Conditional Inclusion Probabilities. Scandinavian Journal of Statistics, 40, 724-733. http://dx.doi.org/10.1111/sjos.12024 [3] Sinha, B.K. (1973) On Sampling Schemes to Realize Preassigned Sets of Inclusion Probabilities of First Two Orders. Calcutta Statistical Association Bulletin, 22, 89-110. [4] Tillé, Y. (2006) Sampling Algorithms. Springer, New York. [5] Brewer, K.R.W. and Hanif, M. (1983) Sampling with Unequal Probabilities. Lecture Notes in Statistics, No. 15, Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4684-9407-5 [6] Wywial, J. (2000) On Precision of Horvitz-Thompson Strategies. Statistics in Transition, 4, 779-798. [7] Bondesson, L., Traat, I. and Lundqvist, A. (2006) Pareto Sampling versus Conditional Poisson and Sampford Sampling. Scandinavian Journal of Statistics, 33, 699-720.
http://dx.doi.org/10.1111/j.1467-9469.2006.00497.x [8] Bondesson, L. (2012) On Sampling with Prescribed Second-Order Inclusion Probabilities. Scandinavian Journal of Statistics, 39, 813-829. http://dx.doi.org/10.1111/j.1467-9469.2012.00808.x