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 co...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.展开更多
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...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,展开更多
基金This project is supported by the National Natural Science Foundation of China
文摘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.
文摘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,
