Dimension reduction in semiparametric regressions includes construction of informative linear combinations and selection of contributing predictors. To reduce the predictor dimension in semiparametric regressions, we propose an ℓ₁-minimization of sliced inverse regression with the Dantzig...

This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An l1 minimization method is used to select the important features from which the LDA will be constructed....

In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric distribution for the data and it does not require the...

The existence of a limiting spectral distribution (LSD) for a large-dimensional sample covariance matrix generated by the vector autoregressive moving average (VARMA) model is established. In particular, we obtain explicit forms of the LSDs for random matrices generated by a first-order vector...