Use of regression method of estimation for estimating mean from incomplete sample

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Use of regression method of estimation for estimating mean from incomplete sample

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Abstract

In this paper we have used Hansen and Hurwitz technique along with Regression method of estimation and developed a better estimator than one suggested by Hansen & Hurwitz. We have also worked out optimum k and n for large N and found same as those for HH estimator. Hansen and Hurwitz (1946) were the first to deal with the problem of the incomplete sample in mail surveys. They proposed a technique, which is useful in finding out unbiased estimates of population parameters in spite of incompleteness of sample responses. Srinath (1971) has extended the Hansen and Hurwitz theory to multiphase sampling.

Keywords: Regression Method of Estimation, mean, Incomplete Sample

Abstract
Introduction
Proposed regression estimator
1. Introduction
2. Mean and variance of the proposed estimator
3. Comparison of new proposed estimator with HH estimator
Comparison of new proposed estimator with HH estimator for fixed cost
1. Definition of cost function
Summary (Conclusion)
References

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[...] and Pandey, S.S.(2003)(b): 'Separate generalized two phase estimator for population mean with post stratification for in presence of non-response', International Conference on Recent Statistical techniques in Life Testing, Reliability, Sampling Theory and Quality Control at B.H.University, Varanasi., (Dec. 29-31, 2003) Khare, B.B. and Sinha, R.R.(2003)(c): class of two-phase sampling estimators for population mean using multi auxiliary characters in presence of non-response', International Conference on Recent Statistical techniques in Life Testing, Reliability, Sampling Theory and Quality Control at B.H.University, Varanasi., (Dec. [...]

[...] ( 3.2 .6) Summary: C0 C1P S ( 3.2 .7) In the present dissertation an attempt has been made to utilize the auxiliary variable, using regression method of estimation, in the Hansen & Hurwitz (1946) problem. The estimator has been proposed and its large sample variance has been obtained. This variance has been optimized for the choice of optimum sample size and optimum the retaining factor, subjected to a suitable linear fixed cost function. It has been observed that the proposed estimator has smaller optimum variance as compared to that of Hansen & Hurwitz (1946) estimator, thereby establishing its use in surveys. [...]

[...] Let and X respectively and yn1 yn ' 2 and and xn1 are the sample mean for respondent class for characters Y be corresponding means for the sub sample taken from the xn' 2 non respondent class. Here we propose the following estimator. * y plr yn byx ( X N xn* ) . ( 2.1 .1) * * Where, yn and xn are means suggested by Hansen and Hurwitz (1946) and are defined as follows. * yn n1 yn1 n2 yn' n1 n x * 2 n1 xn1 n2 xn' n1 n ( 2.1 .2) and byx is sample coefficient of regression of Y on X defined on n1 variables only. [...]

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