ESTIMATING A BOUNDED NORMAL MEAN RELATIVE TO SQUARED ERROR LOSS FUNCTION

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KARIMNEZHAD A.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Journal: Journal of Sciences, Islamic Republic of Iran Year:2011 | Volume:22 | Issue:3 Page(s): 267-276

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Information Journal Paper

Title

ESTIMATING A BOUNDED NORMAL MEAN RELATIVE TO SQUARED ERROR LOSS FUNCTION

Author(s)

KARIMNEZHAD A. | Issue Writer Certificate

Keywords

ADMISSIBILITYQ2

BOUNDED NORMAL MEANQ2

MAXIMUM LIKELIHOOD ESTIMATORQ2

RAO- BLACKWELLIZATIONQ2

SQUARED ERROR LOSSQ2

Abstract

Let X1, ..., Xn be a random sample from a normal distribution with unknown mean q and known variance s2. The usual estimator of the mean, i.e., sample mean, is the MAXIMUM LIKELIHOOD ESTIMATOR which under SQUARED ERROR LOSS function is minimax and admissible estimator. In many practical situations, q is known in advance to lie in an interval, say [-m, m] for some m>0. In this case, the MAXIMUM LIKELIHOOD ESTIMATOR changes and dominates X- but it is no longer admissible. Minimax and some other estimators for this problem have been studied by some researchers. In this paper, a new estimator is proposed and the risk function of it is compared with some other competitors. According to our findings, the use of X- and the MAXIMUM LIKELIHOOD ESTIMATOR is not recommended when some information are accessible about the finite bounds on [-m, m] in advance. Based on the values taken by q in [-m, m], the appropriate estimator is suggested.

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APA: Copy

KARIMNEZHAD, A.. (2011). ESTIMATING A BOUNDED NORMAL MEAN RELATIVE TO SQUARED ERROR LOSS FUNCTION. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 22(3), 267-276. SID. https://sid.ir/paper/84135/en

Vancouver: Copy

KARIMNEZHAD A.. ESTIMATING A BOUNDED NORMAL MEAN RELATIVE TO SQUARED ERROR LOSS FUNCTION. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2011;22(3):267-276. Available from: https://sid.ir/paper/84135/en

IEEE: Copy

A. KARIMNEZHAD, “ESTIMATING A BOUNDED NORMAL MEAN RELATIVE TO SQUARED ERROR LOSS FUNCTION,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 22, no. 3, pp. 267–276, 2011, [Online]. Available: https://sid.ir/paper/84135/en

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