Sampling Techniques-Multistage Sampling and Its Application (ISS Statistics Paper III): Questions 1 - 1 of 1

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Question number: 1

» Sampling Techniques » Multistage Sampling and Its Application

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Consider a population U= {u 1, u 2, …, u n}. Observations of study variable (y) and auxiliary variable (x) are y (u i) =y i, x (u i) =x i, i = 1, 2, . . , N. Let p i =X i /X where X=i=1NXi . A sample of size n is drawn with PPSWR. Show that the population total T=i=1Nyi , the estimator y^pps=1ni=1nyipi is an unbiased estimator. Obtain the variance of the estimator of the population total.

Explanation

Consider a population U= {u 1, u 2, …, u n}. Observations of study variable (y) and auxiliary variable (x) are y (u i) =y i, x (u i) =x i, i = 1, 2, . . , N. Let p i =X… (323 more words) …

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