Bounded Loss Functions and the Characteristic Function Inversion Method for Computing Expected Loss
نویسنده
چکیده
In robust parameter design, the quadratic loss function is commonly used. However, this loss function is not always realistic and the expected loss may not exist in some cases. This paper proposes the use of a general class of bounded loss functions that are cumulative distribution functions and probability density functions. New loss functions are investigated and the loss functions are shown to yield optimal settings different from those obtained with the quadratic loss. For the class of models that are linear in the noise factors, we give a numerical method based on characteristic function inversion for computing expected loss. The method is quick and accurate; thus, it eases computation of the expected loss and comparison of alternative control factor settings. This method is applicable as long as the distributions chosen to represent the loss function and noise factors have tractable characteristic functions.
منابع مشابه
ESTIMATION OF SCALE PARAMETER UNDER A REFLECTED GAMMA LOSS FUNCTION
In this paper, the estimation of a scale parameter t under a new and bounded loss function, based on a reflection of the gamma density function, is discussed. The best scale-invariant estimator of tis obtained and the admissibility of all linear functions of the sufficient statistic, for estimating t in the absence of a nuisance parameter, is investigated
متن کاملRisk premiums and certainty equivalents of loss-averse newsvendors of bounded utility
Loss-averse behavior makes the newsvendors avoid the losses more than seeking the probable gains as the losses have more psychological impact on the newsvendor than the gains. In economics and decision theory, the classical newsvendor models treat losses and gains equally likely, by disregarding the expected utility when the newsvendor is loss-averse. Moreover, the use of unbounded utility to m...
متن کاملAdmissible and Minimax Estimator of the Parameter $theta$ in a Binomial $Bin( n ,theta)$ distribution under Squared Log Error Loss Function in a Lower Bounded Parameter Space
Extended Abstract. The study of truncated parameter space in general is of interest for the following reasons: 1.They often occur in practice. In many cases certain parameter values can be excluded from the parameter space. Nearly all problems in practice have a truncated parameter space and it is most impossible to argue in practice that a parameter is not bounded. In truncated parameter...
متن کاملEstimation of Scale Parameter Under a Bounded Loss Function
The quadratic loss function has been used by decision-theoretic statisticians and economists for many years. In this paper the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant ...
متن کاملEstimating a Bounded Normal Mean Relative to Squared Error Loss Function
Let be a random sample from a normal distribution with unknown mean and known variance 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, is known in advance to lie in an interval, say for some In this case, the maximum likelihood estimator...
متن کامل