Total shrinkage versus partial shrinkage in multiple linear regression

Partial factor modeling: predictor-dependent shrinkage for linear regression

Partial Factor Modeling: Predictor-Dependent Shrinkage for Linear Regression P. Richard Hahn a , Carlos M. Carvalho b & Sayan Mukherjee c a Booth School of Business , University of Chicago , Chicago , IL , 60637 b McCombs School of Business , The University of Texas , Austin , TX , 78712 c Departments of Statistical Science, Computer Science, Mathematics, and Institute for Genome Sciences Polic...

Predictor-dependent shrinkage for linear regression via partial factor modeling

In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, π(Y,X), rather than a purely conditional model, π(Y | X), where Y is a scalar response variable and X is a vector of predictors. This approach is motivated by the fact that in many situations the marginal predictor distribution π(X) can provide useful information about th...

Shrinkage regression

Interquantile Shrinkage in Regression Models.

Conventional analysis using quantile regression typically focuses on fitting the regression model at different quantiles separately. However, in situations where the quantile coefficients share some common feature, joint modeling of multiple quantiles to accommodate the commonality often leads to more efficient estimation. One example of common features is that a predictor may have a constant e...

Shrinkage structure in biased regression

Biased regression is an alternative to ordinary least squares (OLS) regression, especially when explanatory variables are highly correlated. In this paper, we examine the geometrical structure of the shrinkage factors of biased estimators. We show that, in most cases, shrinkage factors cannot belong to [0, 1] in all directions. We also compare the shrinkage factors of ridge regression (RR), pri...