Robust Bayesian prediction and estimation under a squared log error loss function

Kiapour, Azadeh; Nematollahi, Nader

doi:10.1016/j.spl.2011.07.002

Cited by 31 publications

(15 citation statements)

References 12 publications

(7 reference statements)

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“…(b) In the limiting case a → −∞ and b → +∞ estimator (14) minimizes the expectation of squared loss function (1), and in the limiting case a → 0 and b → +∞ estimator (14) minimizes the expectation of precautionary loss function (2).…”

Section: An Interval Symmetric Loss Function and A Bayes Estimatormentioning

confidence: 99%

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Loss functions in restricted parameter spaces and their Bayesian applications

Mozgunov

Jaki

Gasparini

2019

Journal of Applied Statistics

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Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined on a restricted space. It can also be an inappropriate choice in the context when an extreme overestimation and/or underestimation results in severe consequences and a more conservative estimator is preferred. We advocate a class of loss functions for parameters defined on restricted spaces which infinitely penalize boundary decisions like the squared error loss does on the real line. We also recall several properties of loss functions such as symmetry, convexity and invariance. We propose generalizations of the squared error loss function for parameters defined on the positive real line and on an interval. We provide explicit solutions for corresponding Bayes estimators and discuss multivariate extensions. Four well-known Bayesian estimation problems are used to demonstrate inferential benefits the novel Bayes estimators can provide in the context of restricted estimation.

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Section: An Interval Symmetric Loss Function and A Bayes Estimatormentioning

confidence: 99%

“…which was used by many researchers [12,14]. The precautionary loss function covers the case of the scale parameter.…”

Section: Introductionmentioning

confidence: 99%

Loss functions in restricted parameter spaces and their Bayesian applications

Mozgunov

Jaki

Gasparini

2019

Journal of Applied Statistics

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“…So, we elect to restrict attention to a given flexible family of priors and we choose one member from that family, which seems to best match our personal beliefs. Robust Bayesian analysis is connected to the effect of changing a prior within a class Γ for some quantity, for example, the posterior risk, Bayes risk, or posterior expected value, see Kiapour and Nematollahi (2011). Construction of robust Bayesian and shortest robust Bayesian tolerance intervals based on k-record values is currently under investigation.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Equal-tailed and shortest Bayesian tolerance intervals based on exponentialk-records

Kiapour

Qomi

2016

Communications in Statistics - Theory and Methods

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“…For estimation under the loss (1.1), see Sanjari Farsipour & Zakerzadeh (2006), Mahmoudi & Zakerzadeh (2011), Kiapour & Nematollahi (2011), Nematollahi & Jafari Tabrizi (2012) and Zakerzadeh & Moradi Zahraie (2015). Now, suppose that Y 1 , ..., Y n are independent and identically distributed random variables according to the probability distribution function…”

Section: Introductionmentioning

confidence: 99%