Use of Auxiliary Information: Probability Proportional to Size and with Replacement (PPSWR) Sampling

Sarjinder Singh
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Sarjinder Singh: St. Cloud State University, Department of Statistics

Chapter 4 in Advanced Sampling Theory with Applications, 2003, pp 295-348 from Springer

Abstract: Abstract Through the previous chapter we have seen that the proper use of auxiliary information at the estimation stage for estimating any population parameter results in a gain in the efficiency of the resultant estimators. For example, the product and ratio estimators of the population mean remain better than the sample mean when the correlation between the study variable and the auxiliary variable lies in the interval [−1.0,−0.5) and (+0.5, + 1.0], respectively. In this chapter we shall show that the auxiliary information can also be used to select a sample which can provide better estimators of population parameters. In other words, the auxiliary information can be used at the sample selection stage as well as at the estimation stage. A sampling scheme with replacement in which each sampling unit has unequal probability of selection, the probability being proportional to the size of the auxiliary variable associated with the particular unit, is called probability proportional to size and with replacement (PPSWR) sampling scheme.

Keywords: Infant Mortality Rate; Auxiliary Variable; Unbiased Estimator; Total Fertility Rate; Average Price (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-007-0789-4_4

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DOI: 10.1007/978-94-007-0789-4_4

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