Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series


Variable selection and direction estimation for single-index models via DC-TGDR method

Wei Zhong
Xi Liu
Shuangge Ma

This paper is concerned with selecting important covariates
and estimating the index direction simultaneously for
high dimensional single-index models. We develop an efficient
Threshold Gradient Directed Regularization method
via maximizing Distance Covariance (DC-TGDR) between
the single index and response variable. Due to the appealing
property of distance covariance which can measure nonlinear
dependence between random variables, the proposed
method avoids estimating the unknown link function of the
single index and dramatically reduces computational complexity
compared to other methods that use smoothing techniques.
It keeps the model-free advantage from the view of
sufficient dimension reduction and requires neither predictors
nor response variable to be continuous. In addition, the
DC-TGDR method encourages a grouping effect. That is,
it is capable of choosing highly correlated covariates in or
out of the model together. We examine finite-sample performance
of the proposed method by Monte Carlo simulations.
In a real data analysis, we identify important copy number
alterations (CNAs) for gene expression.

Distance covariance, Highdimensional
data, Threshold gradient directed regularization,
Single-index models, Variable selection.

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