Shrinkage preliminary test estimation under a precautionary loss function with applications on records and censored ‎data

Kiapour, Azadeh; Qomi, Mehran Naghizadeh

doi:10.18869/acadpub.jirss.15.2.73

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…Prakash and Singh (2007) and Prakash and Singh (2008) dealt with shrinkage pretest estimation under the LINEX loss in Pareto and exponential distribution, respectively. New researches are in works by Belaghi et al(2015), Naghizadeh Qomi and Barmoodeh (2015) and Kiapour and Naghizadeh Qomi (2016).…”

Section: Introductionmentioning

confidence: 99%

Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

Barmoodeh¹,

Qomi²

2024

Adv Meth Stat

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Considering a Pareto model with unknown shape and scale parameters \(\alpha\) and \(\beta\), respectively, we are interested in Thompson shrinkage test estimation for the shape parameter \(\alpha\) under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for \(\alpha\) and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for \(\alpha\) with the help of a point guess value \(\alpha_0\) and record observations. We investigate the risk-bias of these estimators and compute their risks numerically. A comparison is performed between the PTS estimators and a risk-unbiased estimator. A numerical example is presented for illustrative and comparative purposes. We end the paper by discussion and concluding remarks.

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Section: Introductionmentioning

confidence: 99%

Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

Barmoodeh¹,

Qomi²

2024

Adv Meth Stat

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“…For example, in dam construction, an underestimation of the peak water level is considered much more serious than an overestimation (see Zellner 1986). In such situations, the use of symmetric loss function is inappropriate, see for example, Qomi, Nematollahi, and Parsian (2010), Al-Mosawi and Khan (2018) and Kiapour and Qomi (2016). Let X i1 ; X i2 ; :::; X in i be an independent random sample of size n i from the uniform population p i Uð0; h i Þ, where h i >0 denotes the unknown scale parameter, i ¼ 1; :::; k. Let h ½1 h ½2 Á Á Á h ½k denote the ordered values of h 1 ; :::; h k , so that, the population associated with the largest scale parameter h ½k is called the best population.…”

Section: Introductionmentioning

confidence: 99%

Estimation after Selection from Uniform Populations under an Asymmetric Loss Function

Arshad

Abdalghani

2019

American Journal of Mathematical and Management Sciences

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The problem of estimation after selection arises in the situations where we wish to select a population among k available populations and estimate the parameter of the selected population. This paper considers estimation of the scale parameter h S of the selected uniform population, under the criterion of an asymmetric scale equivariant (ASE) loss function. For selecting the best uniform population, a class of selection rules proposed by Arshad and Misra (2015b) is used. Three natural estimators of h S based on the maximum likelihood estimators, uniformly minimum variance unbiased estimators, and minimum risk equivariant estimators are considered. The generalized Bayes estimator of h S with respect to a non-informative prior is derived. Under the ASE loss function, a general result for improving a scale-equivariant estimator of h S is provided. A consequence of this result, the estimators better than some of the natural estimators are obtained. Also, under the ASE loss function, a subclass of natural-type estimators is shown to be inadmissible for estimating h S. Finally, the risk functions of the various competing estimators of h S are compared via a simulation study.

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“…The value of k near to zero (one) implies a strong belief in the guess value θ 0 (sample values). Significant attention has been paid to the problem of shrinkage estimation, see Prakash and Singh (2008), Naghizadeh Qomi and Barmoodeh (2015), Belaghi et al (2014), Belaghi et al (2015 a, b), Kiapour and Naghizadeh (2016), Baklizi et al (2016), Naghizadeh Qomi (2017a), Safarian et al (2018) and Volterma et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Performance of a Class of Bayes Shrinkage Estimators Based on Rayleigh Record Data under Reflected Gamma Loss Function

Qomi

Dey²,

Fathollahi

2019

JIRSS

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This article addresses the problem of Bayesian shrinkage estimation for the Rayleigh scale parameter based on record values under the reflected gamma loss (RGL) function. A class of Bayesian shrinkage estimators using prior point information is constructed. The risk functions of the maximum likelihood estimator (MLE) and proposed Bayesian shrinkage estimator are derived under the RGL function. The performance of Bayesian shrinkage estimator is compared with the MLE numerically and graphically. One data set has been analyzed to illustrate the performance of the Bayesian shrinkage estimator.

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Shrinkage preliminary test estimation under a precautionary loss function with applications on records and censored ‎data

Cited by 5 publications

References 15 publications

Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

Estimation after Selection from Uniform Populations under an Asymmetric Loss Function

Performance of a Class of Bayes Shrinkage Estimators Based on Rayleigh Record Data under Reflected Gamma Loss Function

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