TY - CHAP
T1 - Some Decision-Theoretic Aspects of Finite Population Sampling
AU - Rinott, Yosef
PY - 2009/1/1
Y1 - 2009/1/1
N2 - This chapter presents a small sample of the extensive literature on decision–theoretic aspects of sampling from finite populations, without attempting to give a comprehensive survey of the best possible results and references. Decision theory provides tools and insights for understanding, comparing, and selecting sampling and estimation procedures. By random sampling, statisticians introduce noise or randomness that did not exist in the original problem. It is well known that the introduction of random sampling can avoid biases and allow important notions such as unbiased estimation and confidence intervals. In the context of finite populations, optimality is most often expressed in terms of minimax results, which in general require random strategies. Other decision–theoretic notions such as loss and risk, admissibility, sufficiency, completeness, un-biasedness, uniformly minimum variance (UMV), Bayes procedures, and more, will also be discussed in connection with finite population sampling. Minimax estimators can be obtained from Bayesian calculations. An example of this approach concerning estimation of a proportion in a finite population is given with the purpose of demonstrating the technique.
AB - This chapter presents a small sample of the extensive literature on decision–theoretic aspects of sampling from finite populations, without attempting to give a comprehensive survey of the best possible results and references. Decision theory provides tools and insights for understanding, comparing, and selecting sampling and estimation procedures. By random sampling, statisticians introduce noise or randomness that did not exist in the original problem. It is well known that the introduction of random sampling can avoid biases and allow important notions such as unbiased estimation and confidence intervals. In the context of finite populations, optimality is most often expressed in terms of minimax results, which in general require random strategies. Other decision–theoretic notions such as loss and risk, admissibility, sufficiency, completeness, un-biasedness, uniformly minimum variance (UMV), Bayes procedures, and more, will also be discussed in connection with finite population sampling. Minimax estimators can be obtained from Bayesian calculations. An example of this approach concerning estimation of a proportion in a finite population is given with the purpose of demonstrating the technique.
UR - http://www.scopus.com/inward/record.url?scp=79954615241&partnerID=8YFLogxK
U2 - 10.1016/S0169-7161(09)00241-7
DO - 10.1016/S0169-7161(09)00241-7
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AN - SCOPUS:79954615241
T3 - Handbook of Statistics
SP - 523
EP - 558
BT - Handbook of Statistics
ER -