Estimators for the Population Mean in the Case of Missing Data

Kadılar, Cem; Çıngı, Hülya

doi:10.1080/03610920701855020

Cited by 51 publications

(19 citation statements)

References 10 publications

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“…Kadilar and Cingi () proposed the following three ratio estimators of the population mean in the form

{\overset{y}{true}}_{KC 1} = \frac{{\overset{y}{true}}_{italics} + b (\overset{true¯}{italicX} - \overset{true¯}{italicx})}{{\overset{true¯}{italicx}}_{s}} \overset{true¯}{italicX}

{\overset{y}{true}}_{KC 2} = \frac{{\overset{y}{true}}_{italics} + b (\overset{true¯}{italicX} - {\overset{x}{true}}_{italics})}{{\overset{true¯}{italicx}}_{s}} \overset{true¯}{italicX}

{\overset{y}{true}}_{KC 3} = \frac{{\overset{y}{true}}_{italics} + b (\overset{true¯}{italicx} - {\overset{x}{true}}_{italics})}{{\overset{true¯}{italicx}}_{s}} \overset{true¯}{italicx}

where

b = \frac{s_{xy}}{{italics}^{2}_{x}} = \frac{\frac{true \sum_{i = 1}^{m (1)} ((), x_{i} - {\overset{true¯}{italicx}}_{s}) ((), y_{i} - {\overset{true¯}{italicy}}_{s})}{italicm ((), 1) - 1}}{true \sum_{j = 1}^{it...}}

…”

Section: Ratio Imputation Under Srsmentioning

confidence: 99%

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Ratio estimators of the population mean with missing values using ranked set sampling

Al-Omari

Bouza

2014

Environmetrics

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The existence of missing observations (MO) is commonly solved by using imputation methods. There are ratio‐based methods for estimating the population mean, while using simple random sampling (SRS), when MO are present. Considering the existence of MO and using of ranked set sampling, we develop a study of the estimation of a population mean using ratio‐based methods. The mean square errors, bias, and gain in accuracy formulas of the suggested estimators are derived. The suggested estimators are compared with their SRS counterpart both theoretically and numerically. Copyright © 2014 John Wiley & Sons, Ltd.

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“…Kadilar and Cingi () proposed the following three ratio estimators of the population mean in the form

{\overset{y}{true}}_{KC 1} = \frac{{\overset{y}{true}}_{italics} + b (\overset{true¯}{italicX} - \overset{true¯}{italicx})}{{\overset{true¯}{italicx}}_{s}} \overset{true¯}{italicX}

{\overset{y}{true}}_{KC 2} = \frac{{\overset{y}{true}}_{italics} + b (\overset{true¯}{italicX} - {\overset{x}{true}}_{italics})}{{\overset{true¯}{italicx}}_{s}} \overset{true¯}{italicX}

{\overset{y}{true}}_{KC 3} = \frac{{\overset{y}{true}}_{italics} + b (\overset{true¯}{italicx} - {\overset{x}{true}}_{italics})}{{\overset{true¯}{italicx}}_{s}} \overset{true¯}{italicx}

where

b = \frac{s_{xy}}{{italics}^{2}_{x}} = \frac{\frac{true \sum_{i = 1}^{m (1)} ((), x_{i} - {\overset{true¯}{italicx}}_{s}) ((), y_{i} - {\overset{true¯}{italicy}}_{s})}{italicm ((), 1) - 1}}{true \sum_{j = 1}^{it...}}

…”

Section: Ratio Imputation Under Srsmentioning

confidence: 99%

“…and σ xy is the covariance between X and Y. The bias is close to zero when Y≅0; m(1) ≅ m, or (R À R σ ) ≅ 0, where R σ ¼ σx σy : Kadilar and Cingi (2008) proposed the following three ratio estimators of the population mean in the form…”

Section: Ratio Imputation Under Srsmentioning

confidence: 99%

Ratio estimators of the population mean with missing values using ranked set sampling

Al-Omari

Bouza

2014

Environmetrics

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“…Lee et al (1994; used the information on an auxiliary variable for the purpose of imputation, Singh and Horn (2000) suggested a compromised method of imputation, Ahmed, Al-Titi, Al-Rawi, and Abu-Dayyeh (2006) suggested several new imputation based estimators that use the information on an auxiliary variable and compared their performances with the mean method of imputation, and Rao and Sitter (1995) used the imputation techniques for variance estimation under two phase sampling. Kadilar and Cingi (2008) and Diana and Perri (2010) also suggested some imputation techniques in case of missing data. In the present study we implicitly assume MCAR.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Population Mean Using Exponential Type Imputation Technique for Missing Observations

Singh

Verma

Sharma

2016

J. Mod. App. Stat. Meth.

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Some imputation techniques are suggested for estimating the population mean when the data values are missing completely at random under a simple random sample without replacement scheme. Two classes of point estimators are proposed. The bias and mean squared error expressions of the proposed point estimators are derived up to first order of approximation. It has been shown that the proposed point estimators are more efficient than some existing point estimators due to Lee, Rancourt, and Sarndal (1994) and Singh and Horn (2000). Theoretical findings are supported by an empirical study based on five populations to show the superiority of the constructed estimators and methods of imputation over others.

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“…Some important works based on imputation method were carried out by [2], [3], [4] and [5]. Later on utilizing the information on an auxiliary variable and using the missing completely at random (MCAR) response mechanism, [6], [7], [8], [9], [10], [11], [12], [13] and [14] among others have suggested several interesting imputation methods with success.…”

Section: Introductionmentioning

confidence: 99%

On the use of imputation methods for missing data in estimation of population mean under two-phase sampling design

Singh¹,

Suman²,

Kadılar³

2018

HJMS

Self Cite

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Non-response is an unavoidable feature in sample surveys and it needs to be carefully handled to avoid the biased estimates of population characteristics/parameters. Imputation is one of the latest fascinating methods which is attracting the attention of survey practitioners to deal with the problems of non-response because it makes the survey data complete before the beginning of generating the survey estimates. The present work proposes some new imputation methods to compensate the missing data in two-phase sampling when non-response observed in samples of both the phases. The proposed imputation methods result in chain type estimators of population mean of study variable and the resultant estimators have shown the ecacious performances in terms of producing the more precise estimates. Properties of the proposed estimators are examined with the help of empirical and simulation studies. Results are critically analyzed and suitable recommendations are put forward to the survey practitioners.

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Estimators for the Population Mean in the Case of Missing Data

Cited by 51 publications

References 10 publications

Ratio estimators of the population mean with missing values using ranked set sampling

Ratio estimators of the population mean with missing values using ranked set sampling

Estimation of Population Mean Using Exponential Type Imputation Technique for Missing Observations

On the use of imputation methods for missing data in estimation of population mean under two-phase sampling design

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