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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
DOI:
https://doi.org/10.15446/rce.v39n2.51586Keywords:
Coefficient of Variation, Shrinkage Estimator, Mean Squared Error, Linear Combination (en)Coeficiente de variación, Combinación lineal, Eficiencia, Error cuadrado medio. (es)
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
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
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.
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.
Palabras clave: coeficiente de variación, combinación lineal, eficiencia, error cuadrado medio.
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References
1. Arnholt, A. T. & Hebert, J. L. (1995), 'Estimating the mean with known coefficient of variation', Journal of the American Statistical Associatio 49, 367-369.
2. Arnholt, A. T. & Hebert, J. L. (2001), 'Combinations of pairs of estimator', Statistics on the Internet, 1-8.
3. Bibby, J. (1972), 'Minimum means square error estimation, ridge regression and some unanswered questions', Progress in Statistics 1, 107-121.
4. Bibby, J. & Toutenburg, H. (1977), Prediction and Improved Estimation in Linear Models, 1 edn, Wiley, New York.
5. Bibby, J. & Toutenburg, H. (1978), 'Improved estimation and prediction', Zeitschriftur Angewandte Mathematik and Mechanik 58, 5-49.
6. Gleser, L. J. & Healy, J. D. (1976), 'Estimating the mean of a normal distribution with known coefficient of variation', Journal of the American Statistical Association 71, 977-981.
7. Kanefuji, K. & Iwase, K. (1998), 'Estimation for a scale parameter with known coefficient of variation', Statistical Papers 39, 377-388.
8. Khan, R. A. (1968), 'A note on estimating the mean of a normal distribution with known coefficient of variation', Journal of the American Statistical Association 63, 1039-1041.
9. Kleffe, J. (1985), Some remarks on improving unbiased estimators by multiplication with a constant, 'Linear Statistical Inference', Cambridge.
10. Laheetharan, A. & Wijekoon, P. (2010), 'Improved estimation of the population parameters when some additional information is available', Statistical Papers 51, 889-914.
11. Laheetharan, A. & Wijekoon, P. (2011), 'Mean square error comparison among variance estimators with known coefficient of variation', Statistical Papers 52, 171-201.
12. Samuel-Cahn, E. (1994), 'Combining unbiased estimators', The American Statistician 48, 34-36.
13. Searls, D. T. (1964), 'The utilization of known coefficient of variation in the estimation procedure', Journal of the American Statistical Association 59, 1225-1226.
14. Searls, D. T. & Intarapanich, P. (1990), 'A note on an estimator for the variance that utilizes the kurtosis', The American Statistician 44, 295-296.
15. Singh, H. P. & Pandit, S. (2008), 'Estimation of the reciprocal of the mean of the inverse gaussian distribution with prior information', Statistica 2, 201-216.
16. Subhash, K. Y. & Cem, K. (2013), 'Improved exponential type ratio estimator of population variance', Revista Colombiana de Estad\'istica 36(1), 145-152.
17. Wencheko, E. & Chipoyera, H. W. (2005), 'Estimation of the variance when kurtosis is known', Statistical Papers 50, 455-464.
18. Wencheko, E. & Wijekoon, P. (2007), 'Improved estimation of the mean in one- parameter exponential families with known coefficient of variation', Statistical Papers 46, 101-115.
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}
}
References
Arnholt, A. T. & Hebert, J. L. (1995), ‘Estimating the mean with known coefficient of variation’, Journal of the American Statistical Associatio 49, 367–369.
Arnholt, A. T. & Hebert, J. L. (2001), ‘Combinations of pairs of estimator’, Statistics on the Internet pp. 1–8.
Bibby, J. (1972), ‘Minimum means square error estimation, ridge regression and some unanswered questions’, Progress in Statistics 1, 107–121.
Bibby, J. & Toutenburg, H. (1977), Prediction and Improved Estimation in Linear Models, 1 edn, Wiley, New York.
Bibby, J. & Toutenburg, H. (1978), ‘Improved estimation and prediction’, Zeitschriftur Angewandte Mathematik and Mechanik 58, 5–49.
Gleser, L. J. & Healy, J. D. (1976), ‘Estimating the mean of a normal distribution with known coefficient of variation’, Journal of the American Statistical Association 71, 977–981.
Kanefuji, K. & Iwase, K. (1998), ‘Estimation for a scale parameter with known coefficient of variation’, Statistical Papers 39, 377–388.
Khan, R. A. (1968), ‘A note on estimating the mean of a normal distribution with known coefficient of variation’, Journal of the American Statistical Association 63, 1039–1041.
Kleffe, J. (1985), Some remarks on improving unbiased estimators by multiplication with a constant, in T. Alinski & W. Klonecki, eds, ‘Linear Statistical Inference’, Cambridge.
Laheetharan, A. & Wijekoon, P. (2010), ‘Improved estimation of the population parameters when some additional information is available’, Statistical Papers 51, 889–914.
Laheetharan, A. & Wijekoon, P. (2011), ‘Mean square error comparison among variance estimators with known coefficient of variation’, Statistical Papers 52, 171–201.
Samuel-Cahn, E. (1994), ‘Combining unbiased estimators’, The American Statistician 48, 34–36.
Searls, D. T. (1964), ‘The utilization of known coefficient of variation in the estimation procedure’, Journal of the American Statistical Association 59, 1225–1226.
Searls, D. T. & Intarapanich, P. (1990), ‘A note on an estimator for the variance that utilizes the kurtosis’, The American Statistician 44, 295–296.
Singh, H. P. & Pandit, S. (2008), ‘Estimation of the reciprocal of the mean of the inverse gaussian distribution with prior information’, Statistica 2, 201–216.
Subhash, K. Y. & Cem, K. (2013), ‘Improved exponential type ratio estimator of population variance’, Revista Colombiana de Estadística 36(1), 145–152.
Wencheko, E. & Chipoyera, H. W. (2005), ‘Estimation of the variance when kurtosis is known’, Statistical Papers 50, 455–464.
Wencheko, E. & Wijekoon, P. (2007), ‘Improved estimation of the mean in one parameter exponential families with known coefficient of variation’, Statistical Papers 46, 101–115.
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