4.1 Auxiliary Data, Ratio Estimator and its Computation STAT 506 - Sampling Theory and Methods

4.1 Auxiliary Data, Ratio Estimator and its Computation STAT 506 - Sampling Theory and Methods

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STAT 506 - Sampling Theory and Methods ANGEL Department of Statistics Eberly College of Science Home // Lesson 4: Auxiliary Data and Ratio Estimation 4.1 Auxiliary Data, Ratio Estimator and its Computation Submitted by gfj100 on Tue, 12/01/2009 - 09:42 Unit Summary Ratio estimator Historical use Example: Apple Juice from Apples Using Auxiliary Information The auxiliary information about the population may include a known variable to which the variable of interest is approximately related. The auxiliary information typically is easy to measure, whereas the variable of interest may be expensive to measure. Population units: 1, 2, . .., N variable of interest : y 1 , y 2 , . .. , y N (expensive or costly to measure) auxiliary variable : x 1 , x 2 , . .. , x N (known) For example consider: A national park is partitioned into N units. y i = the number of animals in unit i x i = the size of unit i Another example might be where a certain city has N bookstores. y i = the sales of a given book title at bookstore i x i = the size of the bookstore i A third example would be a forest that has N trees. y i = the volume of the tree x i = the diameter of the tree
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Ratio Estimators If then, and The ratio estimator, denoted as , is The estimator is useful in the following situation: A. When X and Y are highly linearly correlated through the origin, then: is less than B. The case where N is unknown, then it provides a way to estimate τ y since when N is unknown, one cannot use . Historical Use When was this type of estimator used historically? Probably the first instance of its use occurred in France in 1802. At this time there was no population census and Laplace wanted to estimate the total population of France. He did not have the resources to count every individual so he sampled 30 communities in
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4.1 Auxiliary Data, Ratio Estimator and its Computation STAT 506 - Sampling Theory and Methods

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