Sparse Sliced Inverse Regression Via Lasso
Autor: | Zhigen Zhao, Qian Lin, Jun Liu |
---|---|
Rok vydání: | 2020 |
Předmět: |
Statistics and Probability
Index (economics) Dimensionality reduction 05 social sciences Sufficient dimension reduction Minimax Space (mathematics) 01 natural sciences Article 010104 statistics & probability Lasso (statistics) 0502 economics and business Sliced inverse regression Applied mathematics High-dimensional statistics 0101 mathematics Statistics Probability and Uncertainty 050205 econometrics Mathematics |
Zdroj: | J Am Stat Assoc |
ISSN: | 0162-1459 |
Popis: | For multiple index models, it has recently been shown that the sliced inverse regression (SIR) is consistent for estimating the sufficient dimension reduction (SDR) space if and only if [Formula: see text] , where p is the dimension and n is the sample size. Thus, when p is of the same or a higher order of n, additional assumptions such as sparsity must be imposed in order to ensure consistency for SIR. By constructing artificial response variables made up from top eigenvectors of the estimated conditional covariance matrix, we introduce a simple Lasso regression method to obtain an estimate of the SDR space. The resulting algorithm, Lasso-SIR, is shown to be consistent and achieve the optimal convergence rate under certain sparsity conditions when p is of order o(n(2)λ(2)), where λ is the generalized signal-to-noise ratio. We also demonstrate the superior performance of Lasso-SIR compared with existing approaches via extensive numerical studies and several real data examples. |
Databáze: | OpenAIRE |
Externí odkaz: |