Estimation of inverse mean: An orthogonal series approach
In this article, we propose the use of orthogonal series to estimate the inverse mean space. Compared to the original slicing scheme, it significantly improves the estimation accuracy without losing computation efficiency, especially for the heteroscedastic models. Compared to the local smoothing approach, it is more computationally efficient. The new approach also has the advantage of robustness in selecting the tuning parameter. Permutation test is used to determine the structural dimension. Moreover, a variable selection procedure is incorporated into this new approach, which is particularly useful when the model is sparse. The efficacy of the proposed method is demonstrated through simulations and a real data analysis.
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- Zhu, Yu & Zeng, Peng, 2006. "Fourier Methods for Estimating the Central Subspace and the Central Mean Subspace in Regression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1638-1651, December.
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- Zhu, Lixing & Miao, Baiqi & Peng, Heng, 2006. "On Sliced Inverse Regression With High-Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 630-643, June.
- Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
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