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.

INVERSE REGRESSION METHOD IN DATA STRUCTURE ANALYSIS

In order to explore the nonlinear structure hidden in high-dimensional data, some dimen-sion reduction techniques have been developed, such as the Projection Pursuit technique (PP).However, PP will involve enormous computational load. To overcome this, an inverse regressionmethod is proposed. In this paper, we discuss and develop this method. To seek the interestingprojective direction, the minimization of the residual sum of squares is used as a criterion, andspline functions are applied to approximate the general nonlinear transform function. The algo-rithm is simple, and saves the computational load. Under certain proper conditions, consistencyof the estimators of the interesting direction is shown.

Recent progress on laser-induced breakdown spectroscopy for the monitoring of coal quality and unburned carbon in fly ash

Our recent progress on developments of laser-induced breakdown spectroscopy （L[BS） based equipments for on-line monitoring of pulverized coal and unburned carbon （UC） level of fly ash are reviewed. A fully software-controlled LIBS equipment comprising a self-cleaning device for on-line coal quality monitoring in power plants is developed. The system features an automated sampling device, which is capable of elemental （C, Ca, Mg, Ti, Si, H, Al, Fe, S, and organic oxygen） and proximate analysis （Qad and Aad） through optimal data processing methods. An automated prototype LIBS apparatus has been developed for possible application to power plants for on-line analysis of UC level in fly ash. New data processing methods are proposed to correct spectral interference and matrix effects, with the accuracy for UC level analysis estimated to be 0.26%.

THE STUDY OF RETRIEVAL THEORY AND METHODS FROM SATELLITE REMOTE SENSING FOR METEOROLOGICAL PARAMETERS OVER EASTERN ASIA-PARTI:ISPRM AND SRRM

A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process. the full advantage of every prior information available must be taken.It is necessary to turn the ill- posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.

Asymptotics for Kernel Estimation of Slicing Average Third-Moment Estimation

To estimate central dimension-reduction space in multivariate nonparametric rcgression, Sliced Inverse Regression （SIR）, Sliced Average Variance Estimation （SAVE） and Slicing Average Third-moment Estimation （SAT） have been developed, Since slicing estimation has very different asymptotic behavior for SIR, and SAVE, the relevant study has been madc case by case, when the kernel estimators of SIH and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We. prove the asymptotic normality, and show that, compared with tile existing results, the kernel Slnoothing for SIR, SAVE and SAT has very similar asymptotic behavior,

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.