Abstract
In sampling from a finite population, often the value of some auxiliary variable, closely related to the main characteristic of interest, is available for all the units of the population. This normalized value of the auxiliary variable may be taken as a measure of the size of a unit. For example, in agricultural surveys, the area under a crop may be taken as a size measure of farms for estimating the yield of crops. In such situations, sampling the units with probability proportional to size (PPS) measure with replacement or without replacement may be used in place of simple random sampling with replacement or simple random sampling without replacement. Since the units with larger sizes are expected to have a bigger total of Y, it is expected that PPS measure sampling procedures will be more efficient than SRSWOR or SRSWR. Note that sampling units have an unequal probability of selection. In the sequel, we discuss some common unequal probability sampling procedures.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brewer K.R.W.: A model of systematic sampling with unequal probabilities. Aust. J. Stat. 5, 5–13 (1963)
Durbin, J.: Estimation of sampling error in multi-stage survey. Appl. Stat. 16, 152–164 (1967)
Fellegi, I.P.: Sampling with varying probabilities without replacement: rotating and non-rotating samples. J. Am. Stat. Assoc. 58, 183–201 (1963)
Godambe, V.P.: A unified theory of sampling from finite populations. J. R. Stat. Soc.: Ser. B 17, 267–278 (1955)
Gupta, V.K.: Use of combinatorial properties of block designs in unequal probability sampling. Unpublished Ph.D. thesis, IARI, New Delhi (1984)
Gupta, V.K., Nigam, A.K., Kumar, P.: On a family of sampling schemes with inclusion probability proportional to size. Biometrika 69, 191–196 (1982)
Horvitz, D.G., Thompson, D.J.: A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47, 663–685 (1952)
Koop, J.C.: Contributions to the general theory of sampling finite populations without replacement and with unequal probabilities. Unpublished Ph.D. thesis, North Carolina State College, Raleigh (University Microfilms, Ann Arbor) (1957)
Midzuno, H.: On the sampling system with probability proportional to sum of sizes. Ann. Inst. Stat. Math. 3, 99–107 (1952)
Narain, R.D.: On sampling without replacement with varying probabilities. J. Indian Soc. Agric. Stat. 3(2), 169–175 (1951)
Rao, J.N.K., Hartley, H.O., Cochran,W.G.: On a simple procedure of unequal probability sampling without replacement. J. R. Stat. Soc. B24, 482–491 (1962)
Rao, J.N.K.: On two simple schemes of unequal probability sampling without replacement. Journal of the Indian Statistical Association 3, 173–18 (1965)
Sampford, M.R.: On sampling without replacement with unequal probabilities of selection. Biometrika 54, 499–513 (1967)
Yates, F., Grundy, P.M.: Selection without replacement from within strata with probability proportional to size. J. R. Stat. Soc. B15(2), 53–61 (1953)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Latpate, R., Kshirsagar, J., Kumar Gupta, V., Chandra, G. (2021). Probability Proportional to Size Sampling. In: Advanced Sampling Methods. Springer, Singapore. https://doi.org/10.1007/978-981-16-0622-9_7
Download citation
DOI: https://doi.org/10.1007/978-981-16-0622-9_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-0621-2
Online ISBN: 978-981-16-0622-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)