Dominance of the Positive - Part Shrinkage Estimator when Each Individual Regression Coe ffi cient is Estimated
نویسنده
چکیده
In this paper we consider a regression model and a general family of shrinkage estimators of regression coefficients. We derive the formula for the mean squared error (MSE) of the estimators for each individual regression coefficient. It is shown analytically that the usual shrinkage estimators are dominated by their positivepart variants in terms of MSE.
منابع مشابه
Classic and Bayes Shrinkage Estimation in Rayleigh Distribution Using a Point Guess Based on Censored Data
Introduction In classical methods of statistics, the parameter of interest is estimated based on a random sample using natural estimators such as maximum likelihood or unbiased estimators (sample information). In practice, the researcher has a prior information about the parameter in the form of a point guess value. Information in the guess value is called as nonsample information. Thomp...
متن کاملDifferenced-Based Double Shrinking in Partial Linear Models
Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can ...
متن کاملPositive-Shrinkage and Pretest Estimation in Multiple Regression: A Monte Carlo Study with Applications
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 meth...
متن کاملJackknifed Liu-type Estimator in Poisson Regression Model
The Liu estimator has consistently been demonstrated to be an attractive shrinkage method for reducing the effects of multicollinearity. The Poisson regression model is a well-known model in applications when the response variable consists of count data. However, it is known that multicollinearity negatively affects the variance of the maximum likelihood estimator (MLE) of the Poisson regressio...
متن کاملRobustness Checks and Robustness Tests in Applied Economics
A common exercise in empirical studies is a "robustness check," where the researcher examines how certain "core" regression coe¢ cient estimates behave when the regression speci cation is modi ed by adding or removing regressors. If the coe¢ cients are plausible and robust, this is commonly interpreted as evidence of structural validity. Here, we study when and how one can infer structural vali...
متن کامل