TY - JOUR
T1 - Positive-Shrinkage and Pretest Estimation in Multiple Regression: A Monte Carlo Study with Applications
TT - برآورد مثبت تُربخشی و پیش آزمونی در رگرسیون چندگانه: یک بررسی مونت کارلویی با کاربردها
JF - JIRSS
JO - JIRSS
VL - 10
IS - 2
UR - http://jirss.irstat.ir/article-1-166-en.html
Y1 - 2011
SP - 267
EP - 289
KW - Data analysis
KW - James-Stein estimation
KW - lasso
KW - Monte Carlo simulation
KW - multiple regression
KW - pretest estimation
KW - quadratic risk
KW - RMSE
KW - shrinkage estimation.
N2 - Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is a priori known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage method combines restricted and unrestricted estimators to obtain the parameter estimates. Such an estimator outperforms the classical maximum likelihood estimators. Any prior information may be validated through preliminary test (or pretest), and depending on the validity, may be incorporated in the model as a parametric restriction. Thus, pretest estimator chooses between the restricted and unrestricted estimators depending on the outcome of the preliminary test. Examples using three real life data sets are provided to illustrate the application of shrinkage and pretest estimation. Performance of positive-shrinkage and pretest estimators are compared with unrestricted estimator under varying degree of uncertainty of the prior information. Monte Carlo study reconfirms the asymptotic properties of the estimators available in the literature.
M3
ER -