Skip to main content

Facing sampling techniques as an optimal design problem Cover

.blurhash-client-img { display: none !important; }

Facing sampling techniques as an optimal design problem

Biometrical Letters

Volume 58 (2021): Issue 2 (December 2021)

By: Christos P. Kitsos

Open Access

|Dec 2021

Abstract

The aim of this paper is to investigate and discuss the common points shared, in their line of development, by both Sampling Theory and Design of Experiments. In fact, Sampling Theory adopts the main optimality criterion of the Optimal Design of Experiments, the minimization of variance, i.e. D-optimality. There is also an approach based on c-optimality, as far as ratio estimates are concerned, in Design of Experiments, and the A-optimality involved in a proposed Sampling technique. It is pointed out that the L2 norm is mainly applied as a distance measure.

References

Atkinson A.C. (1969): The use of residuals as a concomitant variable. Biometrika 56, 33-–41.10.1093/biomet/56.1.33
Search in Google Scholar Back to article
Bartlett M.S. (1938): The approximate recovery of information from replicated field experiments with large blocks. The Journal of Agricultural Science 28, 418—427.10.1017/S0021859600050875
Search in Google Scholar Back to article
Bartlett M.S. (1978): Nearest neighbour models in the analysis of field experiments. Journal of the Royal Statistical Society: Series B (Methodological) 40, 147—158.10.1111/j.2517-6161.1978.tb01657.x
Search in Google Scholar Back to article
Beale, E. M. L. (1962): Some uses of computers in operational research. Industrielle Organisation 31, 51—52.
Search in Google Scholar Back to article
Blyth R.C. (1970): On the Inference and Decision Models of Statistics. The Annals of Mathematical Statistics 41(3), 1034—1058.10.1214/aoms/1177696980
Search in Google Scholar Back to article
Cheng C.-S., Li K.-C. (1987). Optimality criteria in survey sampling. Biometrika 74, 337–345.10.1093/biomet/74.2.337
Search in Google Scholar Back to article
Cochran W.G. (2011): Sampling techniques; John Wiley & Sons.
Search in Google Scholar Back to article
Cox D. (1952): Some recent work on systematic experimental designs. Journal of the Royal Statistical Society: Series B 14, 211—219.10.1111/j.2517-6161.1952.tb00114.x
Search in Google Scholar Back to article
Dash P. (2015): Comparison of Some Almost Unbiased Ratio Estimators. Int. Res. J. of Eng. and Tech. (IRJET) 2, 767-–772.
Search in Google Scholar Back to article
Deming W.E.(1990): Sample design in business research; John Wiley & Sons.
Search in Google Scholar Back to article
Dodge Y.(1987): Statistical data analysis based on the L1-norm and related methods; North-Holland, New York.
Search in Google Scholar Back to article
Fedorov V.V. (1972): Theory of optimal experiments; Academic Press, London.
Search in Google Scholar Back to article
Fisher R. (1934): Randomisation, and an old enigma of card play. The Mathematical Gazette 18, 294—297.10.2307/3605473
Search in Google Scholar Back to article
Kendall M G., Stuart A. (1976): The advanced theory of statistics. Hafner Pub. Co. New York.
Search in Google Scholar Back to article
Kish L. (1965): Survey sampling. John Wiley: New York.
Search in Google Scholar Back to article
Kish L. (1976): Optima and proxima in linear sample designs. Journal of the Royal Statistical Society: Series A (General) 139, 80—95.10.2307/2344384
Search in Google Scholar Back to article
Kitsos C.P. (2002): The simple linear calibration problem as an optimal experimental design. Communications in Statistics-Theory and Methods 31, 1167—1177.10.1081/STA-120004915
Search in Google Scholar Back to article
Kitsos C.P. (1999): Calibration. Encyclopedia of Statistical Science, by Kotz, Samuel, Read, Campbell B and Banks, D 3, 62-–65.
Search in Google Scholar Back to article
Kitsos C.P., Müller C.H. (1995): Robust linear calibration. Statistics 27, 93—106.10.1080/02331889508802513
Search in Google Scholar Back to article
Kitsos C.P. (1986): Design and Inference in Nonlinear Problems. Unpublished PhD Thesis. University of Glasgow.
Search in Google Scholar Back to article
Kounias, S. (2016): Jean Papadakis (1903–1997). Proceedings of the 29th Panhellenic Stat. Conference, Thessaloniki and Naousa, 4–7 May 2016, 103—107.
Search in Google Scholar Back to article
Kunert J., Martin R.J. (1987): On the optimality of finite Williams II(a) designs. The Annals of Statistics 15, 1604-–1628.10.1214/aos/1176350613
Search in Google Scholar Back to article
Neyman J., Pearson E.S. (1928): On the use and interpretation of certain test criteria for purposes of statistical inference. Biometrika 20, 263—294.10.1093/biomet/20A.3-4.263
Search in Google Scholar Back to article
Neyman J. (1934): On the two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. J. R. Stat. Soc. 97, 558—625.10.2307/2342192
Search in Google Scholar Back to article
Papadakis J.S. (1937): Méthode statistique pour des expériences sur champ. Institute ď Ameliration Plantes a Salonique. (Greece). Bulletin Scientifique 23, 13—29.
Search in Google Scholar Back to article
Rao J.N.K., Hartley H.O., Cochran W.G. (1962): A simple procedure of unequal probability sampling without replacement. Journal of the Royal Statistical Society: Series B (Methodological) 24, 482-–491.10.1111/j.2517-6161.1962.tb00475.x
Search in Google Scholar Back to article
Reddy V.N. (1974): On a transformed ratio method of estimation. Sankhya C 36, 59—70.
Search in Google Scholar Back to article
Searl D.T. (1964): The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association 59, 1225—1226.10.1080/01621459.1964.10480765
Search in Google Scholar Back to article
Silvey S. (1980): Optimal design. Chapman and Hall.10.1007/978-94-009-5912-5
Search in Google Scholar Back to article
Siscodia B., Dwivedi V. (1981): Modified ratio estimator using coefficient of variation of auxiliary variable. Journal-Indian Society of Agricultural Statistics, 13—18.
Search in Google Scholar Back to article
Som R.K. (1973): A manual of sampling techniques. Heinemann, London.
Search in Google Scholar Back to article
Tarter M.E. (1986): Mean integrated squared error sampling. Journal of the American Statistical Association 81, 234-–242.10.1080/01621459.1986.10478266
Search in Google Scholar Back to article
Tin M. (1965): Comparison of some ratio estimators. Journal of the American Statistical Association 60, 294—307.10.1080/01621459.1965.10480792
Search in Google Scholar Back to article
Torsney B. (1981): Algorithms for a constrained optimization problem with applications in statistics and optimum design., Ph.D. Thesis, University of Glasgow.
Search in Google Scholar Back to article
Valliant R. (1985): Nonlinear prediction theory and the estimation of proportions in a finite population. Journal of the American Statistical Association 80, 631–641.10.1080/01621459.1985.10478163
Search in Google Scholar Back to article
Wynn H.P. (1977a): Minimax purposive survey sampling design. Journal of the American Statistical Association 72, 655—657.10.1080/01621459.1977.10480630
Search in Google Scholar Back to article
Wynn H.P., In Statistical Decision Theory and Related Topics; by Gupta, S. and Moore, D. (Eds). Academic Press. New York. Elsevier: 1977b, 471—478.10.1016/B978-0-12-307560-4.50030-2
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/bile-2021-0009 | Journal eISSN: 2199-577X | Journal ISSN: 1896-3811

Journal RSS Feed

Language: English

Page range: 119 - 131

Published on: Dec 30, 2021

Published by: Polish Biometric Society

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

sampling Theory,

alphabetic optimality criteria,

ratio estimates,

mean square error

Related subjects:

Bioinformatics,

Life sciences, other,

Probability and statistics,

Applied mathematics

© 2021 Christos P. Kitsos, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 58 (2021): Issue 2 (December 2021)

Previous article