CLUSTER-BASED REGULARIZED SLICED INVERSE REGRESSION FOR FORECASTING MACROECONOMIC VARIABLES

This paper concerns the dimension reduction in regression for large data set. The authors introduce a new method based on the sliced inverse regression approach, cMled cluster-based regularized sliced inverse regression. The proposed method not only keeps the merit of considering both response and predictors＇ information, but also enhances the capability of handling highly correlated variables. It is justified under certain linearity conditions. An empirical application on a macroeconomic data set shows that the proposed method has outperformed the dynamic factor model and other shrinkage methods.

On spline approximation of sliced inverse regression

The dimension reduction is helpful and often necessary in exploring the nonparametric regression structure.In this area,Sliced inverse regression (SIR) is a promising tool to estimate the central dimension reduction (CDR) space.To estimate the kernel matrix of the SIR,we herein suggest the spline approximation using the least squares regression.The heteroscedasticity can be incorporated well by introducing an appropriate weight function.The root-n asymptotic normality can be achieved for a wide range choice of knots.This is essentially analogous to the kernel estimation.Moreover, we also propose a modified Bayes information criterion (BIC) based on the eigenvalues of the SIR matrix.This modified BIC can be applied to any form of the SIR and other related methods.The methodology and some of the practical issues are illustrated through the horse mussel data.Empirical studies evidence the performance of our proposed spline approximation by comparison of the existing estimators.

Dimension reduction based on weighted variance estimate

In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.