Abstract
Estimation of the parameter in a finite population based on random sampling may be regarded as a special case of randomized design without errors of measurement. The purpose of this chapter is to present a formulation of the theory of unbiased estimation for the case of sampling from finite populations in the most general setup.
The contents of this chapter was published in the author’s book written in Japanese (Takeuchi (1973) Studies in Some Aspects of Theoretical Foundations of Statistical Data Analysis, Chap. 7). Similar formulation of the problem is given in Sanders et al. (1999) Statistics: a first course, 6th edn.
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References
Basu, D.: On statistics independent of a complete sufficient statistics. Sankhya 15, 377–380 (1955)
Sanders, D., Smidt, R., Adatia, A., Larson, G.: Statistics: A First Course, 6th edn. McGraw Hill, New York (1999)
Takeuchi, K.: Studies in Some Aspects of Theoretical Foundations of Statistical Data Analysis (in Japanese). Toyo Keizai Inc., Tokyo (1973)
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Takeuchi, K. (2020). Some Remarks on General Theory for Unbiased Estimation of a Real Parameter of a Finite Population. In: Contributions on Theory of Mathematical Statistics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55239-0_8
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DOI: https://doi.org/10.1007/978-4-431-55239-0_8
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