Semi-parametric estimation of partially linear single-index models
Journal of Multivariate Analysis
A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE
Computational Statistics & Data Analysis
Successive direction extraction for estimating the central subspace in a multiple-index regression
Journal of Multivariate Analysis
Robust estimation of dimension reduction space
Computational Statistics & Data Analysis
Dimension reduction in functional regression with applications
Computational Statistics & Data Analysis
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Minimum average variance estimation (MAVE, Xia et al. (2002) [29]) is an effective dimension reduction method. It requires no strong probabilistic assumptions on the predictors, and can consistently estimate the central mean subspace. It is applicable to a wide range of models, including time series. However, the least squares criterion used in MAVE will lose its efficiency when the error is not normally distributed. In this article, we propose an adaptive MAVE which can be adaptive to different error distributions. We show that the proposed estimate has the same convergence rate as the original MAVE. An EM algorithm is proposed to implement the new adaptive MAVE. Using both simulation studies and a real data analysis, we demonstrate the superior finite sample performance of the proposed approach over the existing least squares based MAVE when the error distribution is non-normal and the comparable performance when the error is normal.