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(19 citation statements)

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“…Kadilar and Cingi () proposed the following three ratio estimators of the population mean in the form $${\overline{\mathit{y}}}_{\mathit{KC}1}=\frac{{\overline{\mathit{y}}}_{\mathrm{italics}}+\mathit{b}\left(\stackrel{true\xaf}{\mathrm{italicX}}-\stackrel{true\xaf}{\mathrm{italicx}}\right)}{{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}}\stackrel{true\xaf}{\mathrm{italicX}}$$ $${\overline{\mathit{y}}}_{\mathit{KC}2}=\frac{{\overline{\mathit{y}}}_{\mathrm{italics}}+\mathit{b}\left(\stackrel{true\xaf}{\mathrm{italicX}}-{\overline{\mathit{x}}}_{\mathrm{italics}}\right)}{{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}}\stackrel{true\xaf}{\mathrm{italicX}}$$ $${\overline{\mathit{y}}}_{\mathit{KC}3}=\frac{{\overline{\mathit{y}}}_{\mathrm{italics}}+\mathit{b}\left(\stackrel{true\xaf}{\mathrm{italicx}}-{\overline{\mathit{x}}}_{\mathrm{italics}}\right)}{{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}}\stackrel{true\xaf}{\mathrm{italicx}}$$ where $\mathit{b}=\frac{{\mathit{s}}_{\mathit{xy}}}{{{\mathrm{italics}}^{2}}_{\mathit{x}}}=\frac{\frac{true{\sum}_{\mathit{i}=1}^{\mathit{m}\left(1\right)}\left({\mathit{x}}_{\mathit{i}}-{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}\right)\left({\mathit{y}}_{\mathit{i}}-{\stackrel{true\xaf}{\mathrm{italicy}}}_{\mathit{s}}\right)}{\mathrm{italicm}\left(1\right)-1}}{\frac{true{\sum}_{\mathit{j}=1}^{\mathrm{it...}}}{}}$…”

confidence: 99%

“…Kadilar and Cingi () proposed the following three ratio estimators of the population mean in the form $${\overline{\mathit{y}}}_{\mathit{KC}1}=\frac{{\overline{\mathit{y}}}_{\mathrm{italics}}+\mathit{b}\left(\stackrel{true\xaf}{\mathrm{italicX}}-\stackrel{true\xaf}{\mathrm{italicx}}\right)}{{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}}\stackrel{true\xaf}{\mathrm{italicX}}$$ $${\overline{\mathit{y}}}_{\mathit{KC}2}=\frac{{\overline{\mathit{y}}}_{\mathrm{italics}}+\mathit{b}\left(\stackrel{true\xaf}{\mathrm{italicX}}-{\overline{\mathit{x}}}_{\mathrm{italics}}\right)}{{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}}\stackrel{true\xaf}{\mathrm{italicX}}$$ $${\overline{\mathit{y}}}_{\mathit{KC}3}=\frac{{\overline{\mathit{y}}}_{\mathrm{italics}}+\mathit{b}\left(\stackrel{true\xaf}{\mathrm{italicx}}-{\overline{\mathit{x}}}_{\mathrm{italics}}\right)}{{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}}\stackrel{true\xaf}{\mathrm{italicx}}$$ where $\mathit{b}=\frac{{\mathit{s}}_{\mathit{xy}}}{{{\mathrm{italics}}^{2}}_{\mathit{x}}}=\frac{\frac{true{\sum}_{\mathit{i}=1}^{\mathit{m}\left(1\right)}\left({\mathit{x}}_{\mathit{i}}-{\stackrel{true\xaf}{\mathrm{italicx}}}_{\mathit{s}}\right)\left({\mathit{y}}_{\mathit{i}}-{\stackrel{true\xaf}{\mathrm{italicy}}}_{\mathit{s}}\right)}{\mathrm{italicm}\left(1\right)-1}}{\frac{true{\sum}_{\mathit{j}=1}^{\mathrm{it...}}}{}}$…”

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…”

confidence: 99%

“…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.…”

confidence: 99%

“…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.…”

confidence: 99%