Improved Linear Combination of Two Estimators for a Function of Interested Parameter

Estimación eficiente de una función de un parámetro a través de una combinación lineal de dos estimadores

In this paper, we consider the problem of improving the efficiency of alinear combination of two estimators, when the population coefficient of variation is known. We generalized the discussion from the case of a parameter to a function of interested parameter. We show that two estimators obtained from improved linear combination of two estimators and linear combination of two improved estimators are equivalent, in terms of efficiency. We also show that, how one can construct an doubly-improved linear combination of two estimators, when the population coefficient of variation is known.

En este artículo, se considera el problema de mejorar la eficiencia de una combinación lineal de dos estimadores cuando el coeficiente de variación poblacional es conocido. Se generaliza el caso de un solo parámetro al de una función del parámetro. Se muestra que hay equivalencia, en términos de eficiencia, entre usar combinaciones lineales mejoradas y combinaciones lineales de estimadores mejorados. También se muestra como construir una combinación lineal doblemente mejorada cuando el coeficiente de variación poblacional es conocido.

https://doi.org/10.15446/rce.v39n2.51586

Improved Linear Combination of Two Estimators for a Function of Interested Parameter Estimación eficiente de una función de un parámetro a través de una combinación lineal de dos estimadores AFSHIN FALLAH¹, HAMID KHOSHTARKIB²

¹Imam Khomeini International University, Faculty of Basic Sciences, Department of Statistics, Qazvin, Iran. Professor. Email: a.fallah@sci.ikiu.ac.ir
²Imam Khomeini International University, Faculty of Basic Sciences, Department of Statistics, Qazvin, Iran. Researcher. Email: khoshtarkibhamid@yahoo.com

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Abstract

In this paper, we consider the problem of improving the efficiency of a linear combination of two estimators when the population coefficient of variation is known. We generalized the discussion from the case of a parameter to a function of are interested parameter. We show that two estimators obtained from a improved linear combination of two estimators and a linear combination of two improved estimators are equivalent in terms of efficiency. We also show how a doubly-improved linear combination of two estimators can be constructed when the population coefficient of variation is known.

Key words: Coefficient of variation, Mean squared error, Efficiency, Linear combination.

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Resumen

Palabras clave: coeficiente de variación, combinación lineal, eficiencia, error cuadrado medio.

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Texto completo disponible en PDF

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References

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[Recibido en junio de 2015. Aceptado en abril de 2016]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv39n2a05,
    AUTHOR  = {Fallah, Afshin and Khoshtarkib, Hamid},
    TITLE   = {{Improved Linear Combination of Two Estimators for a Function of Interested Parameter}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2016},
    volume  = {39},
    number  = {2},
    pages   = {229-245}
}

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