Open AccessPretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations
Author(s) -
Leila Barmoodeh,
Mehran Naghizadeh Qomi
Publication year - 2017
Publication title -
metodološki zvezki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.127
H-Index - 7
eISSN - 1854-0031
pISSN - 1854-0023
DOI - 10.51936/uivd4115
Subject(s) - estimator , shrinkage , mathematics , mean squared error , pareto principle , statistics , shrinkage estimator , bias of an estimator , point estimation , stein's unbiased risk estimate , point (geometry) , minimum variance unbiased estimator , geometry
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.