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Efficient Factor-Type Estimators of Population Mean in Case of Missing Data and Measurement Error
Estimadores factor tipo de eficientes del de la media de la población en caso de datos faltantes y error de medición
DOI:
https://doi.org/10.15446/rce.v48n1.112391Keywords:
Auxiliary variable, Bias, Chain type estimators, Imputation, Correlated measurement error, Mean Square Error, Percent relative efficiency, Simple random sampling, Study variable, Two-phase sampling. (en)Error cuadrático medio, Eficiencia relativa porcentual, Variable de estudio, Variable auxiliar, Muestreo aleatorio simple, Muestreo bifásico, Sesgo, Estimadores de tipo cadena, Imputación, Error de medición correlacionado. (es)
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In sample surveys, dealing with missingness in data is one of the most frequent problem that can be handled by replacing missing values with some imputed values. In addition to such missingness, oftenly data provided by respondents are under reported or over reported which results to “Measurement Error”. In this paper, we have proposed three modified regression type estimators of population mean, using Factor-Type imputation strategy in two-phase sampling set up to deal with the problem of missing data and measurement error. While proposing our efficient estimators, we have considered two auxiliary variables which have chained correlation with the given study variable. The Bias and Mean Square Error of proposed estimators have been derived up to first order of approximation. The suitable conditions for the superiority of proposed estimators over some existing estimators have been derived. A simulation study is carried out using three artificial data sets to illustrate the supremacy of proposed estimators. Finally, real data set is used to demonstrate the efficiency of proposed estimators in practice.
los datos proporcionados por los encuestados no se informan o se informan en exceso, lo que resulta en un error de medición. En este artículo, hemos propuesto tres estimadores de tipo de regresión modificada de la media de la población, utilizando la estrategia de imputación de tipo factor en el muestreo de dos fases establecido para tratar el problema de los datos faltantes y el error de medición. Al proponer nuestros estimadores eficientes, hemos considerado dos variables auxiliares que tienen una correlación en-cadenada con la variable de estudio dada. El sesgo y el error cuadrático medio de los estimadores propuestos se han derivado hasta el primer orden de aproximación. Se han derivado las condiciones adecuadas para la superioridad de los estimadores propuestos sobre algunos estimadores existentes. Se realiza un estudio de simulación utilizando tres conjuntos de datos artificiales para ilustrar la supremacía de los estimadores propuestos. Finalmente, el conjunto de datos reales se utiliza para demostrar la eficiencia de los estimadores propuestos en la práctica.
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