Shrinkage Testimation in Exponential Distribution based on Records under Asymmetric Squared Log Error Loss

Abstract

Abstract. In the present paper, we study shrinkage testimation for the unknown scale parameter θ > 0 of the exponential distribution based on record data under the asymmetric squared log error loss function. A minimum risk unbiased estimator within the class of the estimators of the form cT m is derived, where T m is the maximum likelihood estimate of θ. Some shrinkage testimators are proposed and their risks are computed. The relative efficiencies of the shrinkage testimators with respect to a minimum risk unbiased estimator of the form cT m under the squared log error loss function are calculated for the comparison purposes. An illustrative example is also presented.

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

“…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).…”

“…Also when ∆ > 1, this loss increases sublinearly, while when 0 < ∆ < 1, it rises rapidly to infinity at zero. The SLEL function is useful in situations where underestimation is more serious than overestimation; see Sanjari Farsipour and Zakerzadeh (2005), Kiapour and Nematollahi (2011) and Naghizadeh Qomi and Barmoodeh (2015).…”

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

“…One can construct shrinkage preliminary test estimators for the parameter θ based on the acceptance or rejection of H 0 . Pandey and Singh (1980), Prakash and Singh (2008), Kibria et al (2010), Ahmed et al (2012), Mirfarah and Ahmadi (2014), Arabi Belaghi et al (2014, 2015a, Naghizadeh Qomi and Barmoodeh (2015) and Hossain and Howlader (2016) considered the problem of shrinkage estimation. The aim of this paper is constructing shrinkage preliminary test estimators in exponential distribution under a precautionary loss function.…”