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Mean Estimation under an Efficient Class of Logarithmic-Type Estimators using Two-Phase Sampling.
Estimación de la media bajo una clase eficiente de estimadores de tipo logarítmico mediante muestreo en dos fases.
DOI:
https://doi.org/10.15446/rce.v49n2.119925Keywords:
Bias;, Efficiency;, Mean square error;, Two-phase sampling. (en)Eficiencia;, Error cuadrático medio;, Muestreo en dos fases;, Sesgo. (es)
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This article introduces an efficient class of logarithmic-type estimators for estimating the population mean of the study variable using the information of the auxiliary variable in two-phase sampling. The bias and mean square error (MSE) expressions of the proposed estimators are derived using the first-order Taylor series approximation, and the corresponding efficiency conditions are established. To validate the theoretical findings, a comprehensive numerical and simulation study is carried out using four real populations and an artificially generated data set. The empirical results reveal that the proposed estimator consistently outperforms the usual mean estimator and several existing estimators in terms of lower MSE and higher percent relative efficiency.
Este artículo presenta una clase eficiente de estimadores de tipo logarítmico para estimar la media poblacional de la variable de interés, utilizando información de una variable auxiliar en el muestreo en dos fases. Se derivan las expresiones del sesgo y del error cuadrático medio (ECM) de los estimadores propuestos mediante una aproximación de primer orden de la serie de Taylor, y se establecen las condiciones de eficiencia correspondientes. Para validar los resultados teóricos, se realiza un estudio numérico y de simulación exhaustivo, empleando cuatro poblaciones reales y un conjunto de datos generado artificialmente. Los resultados empíricos muestran que el estimador propuesto supera sistemáticamente al estimador usual de la media y a varios estimadores existentes, en términos de menor ECM y mayor eficiencia relativa porcentual.
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