TITLE:
A Study on LINEX Loss Function with Different Estimating Methods
AUTHORS:
N. Khatun, M. A. Matin
KEYWORDS:
Gamma Distribution, LINEX Loss Function, Bootstrap Method, Estimation Error, Relative Estimation Error
JOURNAL NAME:
Open Journal of Statistics,
Vol.10 No.1,
January
19,
2020
ABSTRACT: LINEX means linear
exponential loss function which used in the analysis of statistical estimation
and prediction problem which rises exponentially on one side of zero and almost
linearly on the other side of zero. It is used in both overestimation and underestimation
problems. Ali Shadrokh and Hassan Pazira [1] presented Shrinkage estimator in Gamma Type-II Censored Data
under LINEX loss function. In that paper, they have explained
how the LINEX loss function works however no practical or detail explanations
were given in terms of changing the shape parameter and the error function. In
this study we have explained how the LINEX loss function works through
practical or detail explanations in terms of changing the shape parameter and
the error function, also see how the loss
function works with the data generated from gamma distribution through
resampling methods to compare the performance of LINEX loss function considering
the relative estimation error and usual estimation error through generating
random numbers from gamma distribution like randomization method and by using
bootstrapping samples. The very intention is
to find out which resampling method performs well in using the LINEX loss function. Using Monte Carlo
Simulations these estimators are compared. It is doing draw random number from
the gamma distribution and finds the
maximum likelihood estimate of θ is and using this estimator
to explain the LINEX loss function; , or , where c is
the shape parameter andis any estimate of the parameter. The shape of this loss function is determined by the value
of c. In the analysis we use the values of shape parameter c = -0.25, -0.50, -0.75, -1
and c = 0.25, 0.50, 0.75, 1. The same
procedure is done by using bootstrapping method, and finally compared between this two methods. The
relative estimation error should be used instead of the estimation error where
the LINEX loss function works better in both of the cases. Between the two
estimators, bootstrap method is better work because although the
characteristics are same, bootstrap method is more dispersed than
others.