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Optimal Shrinkage Preliminary Test Estimation

Statistical models parameters are estimated in an effort to have knowledge about unknown quantities. In many situations, however, statisticians provide the estimation of the parameters by using not only information based on the sample, but other information as well. This information may be regarded as nonsample information(NSI) or uncertain prior information (UPI) about the parameter of interest. It is advantageous to utilize the NSI in the estimation procedure, especially when the information based on the sample may be rather limited or even the data quality is questionable. But in some experimental cases, it is not certain whether or not this information holds. Consider the data arising from tumor measurements in mice, for example, at various times following injection of carcinogens. Such data should be thought as coming from an in vivo experiment. Biologists are interested in estimating growth rate parameter θ when it suspected a priori that θ = θ0. Such θ0can be obtained directly...

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References and Further Reading

  • Ahmed SE (1992) Shrinkage preliminary test estimation in multivariate normal distributions. J Stat Comput Sim 43:177–195

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  • Ahmed SE (2001) Shrinkage estimation of regression coefficients from censored data with multiple observations. In: Ahmed SE, Reid N (eds) Empirical Bayes and likelihood inference. Springer, NewYork, pp 103–120

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  • Ahmed SE, Hussein AA, Sen PK (2006) Risk comparison of some shrinkage M-estimators in linear models. J Nonparametric Stat 18:401–415

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  • Ahmed SE, Doksum KA, Hossain S, You J (2007) Shrinkage, pretest and absolute penalty estimators in partially linear models. Aust NZ J Stat 49:435–454

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  • Bancroft TA (1944) On biases in estimation due to the use of preliminary tests of significance. Ann Math Stat 15:190–204

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  • Berkson J (1942) Test of significance considered as evidence. J Am Stat Assoc 37:325–335

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  • Judge GG, Bock ME (1978) The statistical implication of pre-test and Stein-rule estimators in econometrics. North-Holland, Amsterdam

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© 2011 Springer-Verlag Berlin Heidelberg

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Ahmed, S.E., Chitsaz, S., Fallahpour, S. (2011). Optimal Shrinkage Preliminary Test Estimation. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_431

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