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Statistical Inference: A Short Course by Michael J. Panik

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Appendix 9.A Ratio Estimation

A procedure that is akin to that employed to estimate a population proportion p is ratio estimation. It can be used to determine a population ratio proper or to estimate a population mean. Ratio estimation involves taking measurements on two characteristics of interest of a sampling unit—one corresponding to the numerator and the other corresponding to the denominator of the ratio. In this regard, let a sample of size n consist of the n ordered pairs of observations (Xi, Yi,), i = 1,. . .,n, where the sample values Y1,. . .,Yn refer to some measurable characteristic of the sampling unit that appears in the numerator of the ratio, and the sample values X1,. . .,Xn pertain to some measurable characteristic of the sampling unit that appears in the denominator of the ratio. In what follows, the Xi's will serve as subsidiary information used for ratio estimation purposes.

At this point, some notation is in order. Let the population ratio appear as follows:

(9.A.1) equation

where the population totals for the Y- and X-characteristics are denoted as img and img, respectively, and and are the respective means for the said characteristics. Then an estimator for R is the sample ...

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