Allocating Loss of Precision in the Sample Mean to Wrong Weights and Redundancy in Sampling with Replacement from a Finite Population

2006 ◽  
pp. 575-581
Author(s):  
J. L. Hodges ◽  
Frederick Mosteller ◽  
Cleo Youtz
Keyword(s):  
Finite Population ◽  
Sample Mean

scholarly journals Estimation of finite population distribution function with dual use of auxiliary information under non-response

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243584
Author(s):  
Sardar Hussain ◽  
Sohaib Ahmad ◽  
Sohail Akhtar ◽  
Amara Javed ◽  
Uzma Yasmeen
Keyword(s):  
Distribution Function ◽  
Finite Population ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Distribution Functions ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Sample Distribution

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.

scholarly journals Some Median Type Estimators to Estimate the Finite Population Mean

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.

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

1980 ◽  
Vol 29 (1-2) ◽  
pp. 35-44 ◽  
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.

Use of Statistical Models for the Estimation of Abundance from Groundfish Trawl Survey Data

1990 ◽  
Vol 47 (5) ◽  
pp. 894-903 ◽  
Author(s):  
Stephen J. Smith
Keyword(s):  
Statistical Models ◽  
Gadus Morhua ◽  
Finite Population ◽  
Trawl Survey ◽  
Survey Area ◽  
Sample Mean ◽  
Population Mean ◽  
Model Based ◽  
Design Consistency ◽  
Trawl Surveys

Estimates of fish abundance from stratified random trawl surveys are highly variable and a number of estimators from various statistical models have been suggested to provide more precise estimates. However, model-based estimates of the survey finite population mean which are not based on the sample mean, can be biased and nonrobust to deviations from the model. This is demonstrated in particular for estimates based on the Δ-distribution. A criterion known as asymptotic design consistency (ADC) is presented for selecting those models that can provide estimates of the finite population mean which are asymptotically robust to deviations from the model. The concept of a predictive estimate is presented as a means of incorporating models into an estimate of the finite population mean which can provide more information than the sample mean. Predictive estimates use statistical models to relate the abundance measured in the sample to covariates measured over the whole survey area. This paper demonstrates that consistent relationships exist between the catch of age 4 cod (Gadus morhua) in the survey trawl and concurrently measured hydrographic covariates which can be used to construct model-based ADC predictive estimates of the finite population mean.

scholarly journals Efficient Class of Estimators for Finite Population Mean using Auxiliary Information in Two-Occasion Successive Sampling

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
G. N. Singh ◽  
Mohd Khalid
Keyword(s):  
Linear Combination ◽  
Finite Population ◽  
Auxiliary Information ◽  
Successive Sampling ◽  
Sample Mean ◽  
Population Means ◽  
Population Mean ◽  
Practical Applications ◽  
Optimum Estimator ◽  
Class Of Estimators

In the case of sampling on two occasions, a class of estimators is considered which uses information on the first occasion as well as the second occasion in order to estimate the population means on the current (second) occasion. The usefulness of auxiliary information in enhancing the efficiency of this estimation is examined through the class of proposed estimators. Some properties of the class of estimators and a strategy of optimum replacement are discussed. The proposed class of estimators were empirically compared with the sample mean estimator in the case of no matching. The established optimum estimator, which is a linear combination of the means of the matched and unmatched portions of the sample at the current occasion, was empirically compared with the proposed class of estimators. Mutual comparisons of the proposed estimator were carried out. Suitable recommendations are made to the survey statistician for practical applications.

scholarly journals Modified Ratio-Cum-Product Estimators of Population Mean Using Two Auxiliary Variables

2020 ◽  
pp. 55-65
Author(s):  
J. O. Muili ◽  
E. N. Agwamba ◽  
Y. A. Erinola ◽  
M. A. Yunusa ◽  
A. Audu ◽  
...  
Keyword(s):  
Random Sampling ◽  
Finite Population ◽  
Simple Random Sampling ◽  
Degree Of Approximation ◽  
Ratio Estimator ◽  
Auxiliary Variables ◽  
Sampling Without Replacement ◽  
Sample Mean ◽  
Population Mean ◽  
Product Estimator

A percentile is one of the measures of location used by statisticians showing the value below which a given percentage of observations in a group of observations fall. A family of ratio-cum-product estimators for estimating the finite population mean of the study variable when the finite population mean of two auxiliary variables are known in simple random sampling without replacement (SRSWOR) have been proposed. The main purpose of this study is to develop new ratio-cum-product estimators in order to improve the precision of estimation of population mean in sample random sampling without replacement using information of percentiles with two auxiliary variables. The expressions of the bias and mean square error (MSE) of the proposed estimators were derived by Taylor series method up to first degree of approximation. The efficiency conditions under which the proposed ratio-cum-product estimators are better than sample man, ratio estimator, product estimator and other estimators considered in this study have been established. The numerical and empirical results show that the proposed estimators are more efficient than the sample mean, ratio estimator, product estimator and other existing estimators.

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