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.