Some Improved Ratio and Regression Type Estimators in Case of Non-Response
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Date
2022-11
Authors
Wani, Zakir Hussain
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Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu
Abstract
In sample surveysgenerallyit is not possible that sample will represent population truly, which results in two types of errors viz. (i) sampling error, and (ii) non-sampling error.Non-response is a type ofnon-sampling error. The present investigation entitled“Some Improved Ratio and Regression Type Estimators in case of Non-Response” has been undertaken with the objectives to develop some improved types of separateand combined ratio as well asregression estimatorsfor estimating the population mean in presence of non-response, using auxiliary information, for four cases. The expressions for bias and mean square error (MSE) of proposed estimatorshave been derived up to first order of approximation. Theoretical comparisons of proposed estimators with the usual unbiased estimator by Hansen and Hurwitz (1946) and other existing estimators have been made. The theoretical results are supported by numerical data that demonstrate the superiority of the proposed estimators over existing estimators in terms of mean square errors.
For Case I (non-response occurs on both the study variable (Y) and the auxiliary variable (X), and the population mean X ̅ is known) the separate andcombinedratio estimators t_1^(*(i))andt_2^(*(i)),i=1 to 10,respectively,separate and combined regression estimatorst_3^(*(i)) andt_4^(*(i)),i=1 to 5,respectively,have been proposed. ForCase II (non-response occurs on Y only, information on X is obtained from all the sample units and X ̅ is known) the separate and combined ratio estimatorst_1^('(i)) and t_2^('(i)),i=1 to 10, respectively,separate and combined regression estimatorst_3^('(i)) andt_4^('(i)),i=1 to 5,respectively,have been proposed. For Case III (non-response occurs on both Y and X, but X ̅ is unknown) the separate and combined ratio estimatorst_5^* andt_6^*, separate and combined regression estimatorst_7^(*(i)) andt_8^(*(i)),i=1 to 12, respectively,have been proposed.For Case IV(non-response occurs on Y, information on X is obtained from all the sample units, but the Mean X ̅ is unknown) the separate and combined ratio estimators t_5^'andt_6^', separate and combined regression estimatorst_7^('(i)) and t_8^('(i)),i=1 to 12,respectively, have been proposed. Based on percent relative efficiency, all the proposed estimators are found to be more efficient than the Hansen and Hurwitz (1946) and other existing estimators like, classical separate and combined ratio as well as regression estimators, estimators proposed by Onyekaet al. (2019)and other researchersin respective cases.
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Preferred for your work Zakir Hussain wani 2022. Some Improved Ratio and Regression Type Estimators in case of Non-Response.