The nature of simple random sampling

Mitra, S. K. ; Pathak, P. K. (1984) The nature of simple random sampling Annals of Statistics, 12 (4). pp. 1536-1542. ISSN 0090-5364

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Related URL: http://dx.doi.org/10.1214/aos/1176346810

Abstract

As an estimator of the population mean, the sample mean based only on the distinct units possesses a remarkable invariance property. Under three forms of simple random sampling, viz. simple random sampling without replacement (SRSWOR), simple random sampling with replacement (SRSWR), and fixed cost simple random sampling (SRSFC), it is admissible and unbiased; and asymptotically normally distributed if and only if the Erdos-Renyi-Hajek condition is satisfied. An important implication of this invariance is that for estimating the population mean, these forms of simple random sampling are asymptotically equally cost-efficient. However, from a practical point of view SRSFC does seem to provide greater flexibility in large surveys.

Item Type:Article
Source:Copyright of this article belongs to Institute of Mathematical Statistics.
Keywords:Simple Random Sampling; Sample Mean; Asymptotic Normality; The Erdos-renyi-hajek Condition; Fixed Cost Sampling; Cost-adjusted Efficiency
ID Code:31997
Deposited On:30 Mar 2011 12:58
Last Modified:17 May 2016 14:45

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