Sparse Sliced Inverse Regression via Cholesky Matrix Penalization

We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of central subspace. The estimators use decomposition covariance covariates include regularization term objective function to achieve computationally efficient manner. establish theoretical values tuning parameters that estimation variable selection consistency Furthermore, we propose projection information criterion select parameter our proposed prove facilitates consistency. inherits strength Matrix Lasso estimator; it has superior performance numerical studies can be adapted other sufficient dimension methods literature.