Abstract
In this paper, we introduce a two-step procedure, in the context of ultrahigh-dimensional additive models, to identify nonzero and linear components. We first develop a sure independence screening procedure based on the distance correlation between predictors and marginal distribution function of the response variable to reduce the dimensionality of the feature space to a moderate scale. Then a double penalization based procedure is applied to identify nonzero and linear components, simultaneously. We conduct extensive simulation experiments to evaluate the numerical performance of the proposed method and analyze a cardiomyopathy microarray data for an illustration. Numerical studies confirm the fine performance of the proposed method for various semiparametric models.
Highlights
Suppose we have a random sample, 1 ≤ i ≤ n, where yi is the response variable and is a p-dimensional covariate vector
We propose a more robust approach, called robust distance correlation sure independence screening (RDC-SIS), to reduce dimensionality which ranks each covariate through its distance correlation with the marginal distribution function of the response variable
We propose a robust feature screening procedure for model (2) using distance correlation between predictors and marginal distribution function of response variable
Summary
Suppose we have a random sample (yi, xi1, . . . , xip), 1 ≤ i ≤ n, where yi is the response variable and (xi1, . . . , xip) is a p-dimensional covariate vector. We propose a more robust approach, called robust distance correlation sure independence screening (RDC-SIS), to reduce dimensionality which ranks each covariate through its distance correlation with the marginal distribution function of the response variable This method is model-free and we can expect that the procedure works well for skew or heavy tailed response variable. We propose a robust feature screening procedure for model (2) using distance correlation between predictors and marginal distribution function of response variable. For two univariate normal random variables U and V , with the Pearson correlation coefficient ρ, Szekely, Rizzo, and Bakirov [18] showed that dcorr(U, V ) is strictly increasing in |ρ| This property implies that the distance correlation based feature screening procedure is equivalent to the marginal Pearson correlation learning for linear regression with normally distributed predictors and random error.
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