One- and two-term edgeworth expansions for a finite population sample mean. Exact results. I

In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.

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Some Median Type Estimators to Estimate the Finite Population Mean

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2020/v7i430192 ◽

2020 ◽

pp. 48-58

Author(s):

Waqar Hafeez ◽

Javid Shabbir ◽

Muhammad Taqi Shah ◽

Shakeel Ahmed

Keyword(s):

Linear Regression ◽

Finite Population ◽

Auxiliary Variable ◽

Maximum Efficiency ◽

Order Of Approximation ◽

Study Variable ◽

Sample Mean ◽

First Order ◽

Regression Estimators ◽

Class Of Estimators

Researchers always appreciates estimators of finite population quantities, especially mean, with maximum efficiency for reaching to valid statistical inference. Apart from ratio, product and regression estimators, exponential estimators are widely considered by survey statisticians. Motivated from the idea of exponential type estimators, in this article, we propose some new estimators utilizing known median of the study variable with mean of auxiliary variable. Theoretical properties of the suggested estimators are studied up to first order of approximation. In addition, an empirical and simulation study the comparison of median based proposed class of estimators with sample mean, ratio and linear regression estimators are discussed. The results expose that the proposed estimators are more efficient than the existing estimators.

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On the Admissibility of the Symmetrized Des Raj Estimator for PPSWOR Samples of Size Two

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319800103 ◽

1980 ◽

Vol 29 (1-2) ◽

pp. 35-44 ◽

Cited By ~ 2

Author(s):

S. Sengupta

Keyword(s):

Population Size ◽

Sampling Design ◽

Finite Population ◽

Ratio Estimator ◽

Population Total ◽

Sample Mean ◽

Unbiased Estimators ◽

Linear Estimators

The symmetrized Des Raj estimator for a finite population total based on a PPSWOR sample of size two is shown to be admissible within (i) the class of all linear estimators and (ii) the class of all unbiased estimators. In this connection we have obtained a class of admissible linear estimators of the population total which includes the sample mean multiplied by the population size and the classical ratio estimator for any arbitrary sampling design.

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