Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response

doi:10.1080/00949655.2018.1464571

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Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response

Journal Article•DOI•

Optimized estimation for population mean using conventional and non-conventional measures under the joint influence of measurement error and non-response

Muhammad Irfan¹, Maria Javed¹, Zhengyan Lin²•Institutions (2)

Government College University, Faisalabad¹, Zhejiang University²

22 Apr 2018-Journal of Statistical Computation and Simulation (Taylor & Francis)-Vol. 88, Iss: 12, pp 2385-2403

TL;DR: Most of the research work in the theory of survey sampling only deals with the sampling errors under the assumptions: (i) there is a complete response and (ii) recorded information from individuals as mentioned in this paper.

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Abstract: Most of the research work in the theory of survey sampling only deals with the sampling errors under the assumptions: (i) there is a complete response and (ii) recorded information from individuals...

...read moreread less

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Book•

Estimation in the Presence of Measurement Errors

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Lwando Kondlo

28 Feb 2011

TL;DR: In this article, the problem of estimating the population distribution of independent random variables from error-contaminated samples is considered, where the measurement error is also assumed to be normally distributed.

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Abstract: This study considers the problem of estimating the population distribution of independent random variables from error-contaminated samples. The measurement error is also assumed to be normally distributed. Since the observed distribution function is a convolution of the error distribution with the true underlying distribution, estimation of the latter is often referred to as a deconvolution problem. A thorough study of the relevant deconvolution literature in statistics is reported. The intention is to draw more specific connections between certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error.

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34 citations

Journal Article•DOI•

Estimation of Population Median under Robust Measures of an Auxiliary Variable

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Muhammad Irfan¹, Maria Javed¹, Sandile Charles Shongwe², Muhammad Zohaib¹, Sajjad Haider Bhatti¹ - Show less +1 more•Institutions (2)

Government College University, Faisalabad¹, University of the Free State²

16 Sep 2021-Mathematical Problems in Engineering

TL;DR: In this article, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable, such as decile mean, Hodges-Lehmann estimator, and trimean of an auxiliary variable.

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Abstract: In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.

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1 citations

DOI•

Combined Type Generalized Classes of Efficient Estimators of Mean in Joint Presence of Measurement Error and Non-response using Stratified Two-Phase Sampling

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Aamir Sanaullah, Shaista Sabir

03 Feb 2022-Scientia Iranica

TL;DR: In this article , three classes of generalized and more efficient combined regression-cum-ratio estimators are presented to estimate the population mean of the study variable in stratified two-phase sampling considering non-response and measurement error are present jointly.

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Journal Article•DOI•

Efficient Estimation of Mean in Two-Phase Sampling when Measurement Error and Non-Response are Simultaneously Present

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Shaista Sabir, Aamir Sanaullah

21 Apr 2022-Proceedings of the National Academy of Sciences, India. Section A, Physical sciences

Journal Article•DOI•

Two new estimators of finite population variance under random non-response: An application

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Alisha Mittal, Rajesh Kumar

24 Mar 2023-Model Assisted Statistics and Applications

TL;DR: In this paper , the estimation of finite population variance in simple random sampling without replacement (SRSWOR) in presence of non-response by proposing two estimators (dual to ratio and ratio cum dual to ratio type) have been proposed on the basis of availability and non-availability of auxiliary information.

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Abstract: In this paper, an attempt has been made to study the estimation of finite population variance in simple random sampling without replacement (SRSWOR) in presence of non-response by proposing two estimators. The two estimators (dual to ratio and ratio cum dual to ratio type) have been proposed on the basis of availability and non-availability of auxiliary information. The properties such as bias and mean square error of the proposed estimators have also been studied up to first order of approximation. The proposed estimators are compared with some existing estimators and are also mutually compared. An empirical study, based on both vegetable crop data and simulated data, has been performed to find out the best estimator. It has been seen that out of the two proposed estimators, the ratio cum dual to ratio type estimator performed better than dual to ratio estimator.

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References

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Journal Article•DOI•

The problem of non-response in sample surveys.

[...]

Morris H. Hansen, William N. Hurwitz

01 Dec 1946-Journal of the American Statistical Association

TL;DR: A technique which combines the advantages of both procedures is indicated, and under reasonable assumptions as to the relative costs of the two methods of canvass, an allocation of the sample can be made to mail and field canvasses.

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Abstract: The mail questionnaire is used in a number of surveys because of the economies involved. The principal objection to this method of collecting factual information is that it generally involves a large non-response rate, and an unknown bias is involved in any assumption that those responding are representative of the combined total of respondents and non-respondents. Personal interviews generally elicit a substantially complete response, but the cost per schedule is, of course, considerably higher than it would be for the mail questionnaire method. The purpose of this paper is to indicate a technique which combines the advantages of both procedures. The principle followed is to mail schedules in excess of the number expected to be returned, and to follow up by enumerating a sample of those that do not respond to the mail canvass. Under reasonable assumptions as to the relative costs of the two methods of canvass, an allocation of the sample can be made to mail and field canvasses. An illustration i...

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529 citations

"Optimized estimation for population..." refers background or methods in this paper

...• In case of non-response, an assumption has beenmade that when the subsample of nonrespondents is contacted again through interview they responded due to Hansen and Hurwitz [1]....
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...Keeping this reality in mind, some notable efforts for the estimation of population parameters in the presence of non-response were carried out by Hansen and Hurwitz [1], Srinath [2], Cochran [3], Rao [4], Khare and Srivastava [5], Singh and Kumar [6–8], Singh et al....
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...PRE’s of the estimators with respect to the Hansen and Hurwitz [1] estimator ȳ∗ for Population I....
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...The traditional Hansen and Hurwitz [1] estimator along with its variance is given by...
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...Per cent relative efficiencies (PREs) of the estimators with respect to Hansen and Hurwitz [1] are computed through the expression given in (25)....
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Journal Article•DOI•

Errors of Measurement in Statistics

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William G. Cochran

01 Nov 1968-Technometrics

TL;DR: This review of some of the recent work in the study of errora of measurement focuses on the type of mathematical model used, the extent to which standard techniques of analysis become erroneous and misleading if certain types of errors are present, and the techniques that are available for the numerical study of errors of measurement.

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Abstract: In this review of some of the recent work in the study of errora of measurement, attention is centered on the type of mathematical model used to represent errom of measurement, on the extent to which standard techniques of analysis become erroneous and misleading if certain types of errors are present (and the possible remedial procedures), and the techniques that are available for the numerical study of errors of measurement

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449 citations

Journal Article•DOI•

Transformed ratio type estimators for the population mean in the presence of nonresponse

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B. B. Khare¹, S.P. Srivastava¹•Institutions (1)

Banaras Hindu University¹

01 Jan 1997-Communications in Statistics-theory and Methods

TL;DR: In this article, two transformed ratio type estimators for the populaion mean in presence of non-response were proposed and the proporties of these estimators are studied in the case of a Unite population and also through the superpopulation model approach.

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Abstract: In this paper we have proposed two transformed ratio type estimators for the populaion mean in presence of non-response. The proporties of these estimators are studied in the case of a Unite population and also through the superpopulation model Approach.

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103 citations

"Optimized estimation for population..." refers methods in this paper

...Keeping this reality in mind, some notable efforts for the estimation of population parameters in the presence of non-response were carried out by Hansen and Hurwitz [1], Srinath [2], Cochran [3], Rao [4], Khare and Srivastava [5], Singh and Kumar [6–8], Singh et al. [9], Kumar and Chatterjee [10], Kumar [11] and others....
[...]
...Keeping this reality in mind, some notable efforts for the estimation of population parameters in the presence of non-response were carried out by Hansen and Hurwitz [1], Srinath [2], Cochran [3], Rao [4], Khare and Srivastava [5], Singh and Kumar [6–8], Singh et al....
[...]
...[5] Khare B, Srivastava S. Transformed ratio type estimators for the population mean in the presence of nonresponse....
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Journal Article•DOI•

A regression approach to the estimation of the finite population mean in the presence of non-response

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Housila P. Singh, Sunil Kumar

01 Dec 2008-Australian & New Zealand Journal of Statistics

TL;DR: In this paper, the authors presented various estimators for estimating the population mean of the study variable y using information on the auxiliary variable x in the presence of non-response, and compared with those of existing estimators.

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Abstract: Summary This paper presents various estimators for estimating the population mean of the study variable y using information on the auxiliary variable x in the presence of non-response. Properties of the suggested estimators are studied and compared with those of existing estimators. It is shown that the estimators suggested in this paper are among the best of all the estimators considered. An empirical study is carried out to demonstrate the performance of the suggested estimators and of others, and it is found that the empirical results support the theoretical study.

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70 citations

"Optimized estimation for population..." refers background in this paper

...[20] Kumar S, Bhougal S, Nataraja NS, et al. Estimation of population mean in the presence of non-response and measurement error....
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...[9] Singh HP, Kumar S, Kozak M. Improved estimation of finite-population mean using sub- sampling to deal with non response in two-phase sampling scheme....
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...[21] Kumar S. Improved estimation of population mean in presence of nonresponse and measurement error....
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...(6) Contribution inMSEdue toMEandnon-response is clearly depicted in the following table: Measurement Error Present Absent Non-response Present λ2S2U(2) λ2S 2 Y(2) Absent λ1Ȳ2 ( S2U Ȳ2 + S 2 V X̄2 ) λ1Ȳ2(C2Y + C2X − 2ρYXCYCX ) Given below is the estimator of population mean and its mean square error proposed by Singh and Kumar [6]: ȳSK = ȳ∗ ( X̄ x̄∗ )( X̄ x̄ ) (7) 2390 M. IRFAN ET AL....
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...[11] Kumar S. Efficient use of auxiliary information in estimating the population ratio, product and mean in the presence of non-response....
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Journal Article•DOI•

Multiphase Sampling in Nonresponse Problems

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K. P. Srinath¹•Institutions (1)

Bangalore University¹

01 Sep 1971-Journal of the American Statistical Association

TL;DR: In this article, a sampling procedure involving subsampling of nonrespondents is discussed, under which the subs sampling fraction is not kept constant, but varied according to the sample nonresponse rates.

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Abstract: The sampling procedure involving subsampling of nonrespondents is discussed. A rule for selecting a subsample of nonrespondents is proposed under which the subsampling fraction is not kept constant, but varied according to the sample nonresponse rates. Using this sampling rule, the variance of the estimator of the population mean is independent of the unknown rate of nonresponse in the population. This rule provides a procedure for determining the initial sample size and subsampling fraction in order to have a desired precision of the estimator when the rate of nonresponse is not accurately known. Similar sampling rules for the selection of subsamples when several attempts are made for obtaining information are also proposed.

...read moreread less

50 citations