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On consistency and sparsity for sliced inverse regression in high dimensions. (English) Zbl 1395.62196

Sliced Inverse Regression is a technique for dimension reduction of a dataset \(X\) with dimensions \((n \times p)\) based on a response variable \(y\). In this paper the authors prove that, under mild conditions, the SIR is consistent if and only if \(\lim p/n\) is \(0\). When this condition is not satisfied, a new procedure called DT-SIR (Diagonal Thresholding SIR) is introduced. The DT-SIR is proved to be consistent under some additional assumptions.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
62G20 Asymptotic properties of nonparametric inference
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References:

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