as095-soln

as095-soln - STAT 854/454 Short Solutions to Assignment 5...

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Unformatted text preview: STAT 854/454 Short Solutions to Assignment 5 1. Suppose the finite population follows the model ( ): y i = x i + i , i = 1 , 2 , ,N , where x i > 0 and the i s are independent random variables with E ( i ) = 0 and V ( i ) = x i 2 . The finite population mean x for the auxiliary variable x is known. Let { ( y i ,x i ) ,i s } be a random sample obtained using a probability sampling design. (a) Show that the weighted least square estimator of under the model is given by = y/ x . (b) Show that y = x is a model-unbiased prediction estimator for the finite population mean y . (c) Find the model-based variance V ( y- y ). Soln: Need to use the independence of y 1 , ,y N from the model, y- y = 1 n x x- n N X i s y i- 1 N X i/ s y i , to obtain V ( y- y ) = 2 x n x- x N !...
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as095-soln - STAT 854/454 Short Solutions to Assignment 5...

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