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Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Variable selection is fundamental to high-dimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationallyExpand
Sure independence screening for ultrahigh dimensional feature space
Summary. Variable selection plays an important role in high dimensional statistical modelling which nowadays appears in many areas and is key to various scientific discoveries. For problems of largeExpand
Design-adaptive Nonparametric Regression
  • J. Fan
  • Mathematics
  • 1 December 1992
Abstract In this article we study the method of nonparametric regression based on a weighted local linear regression. This method has advantages over other popular kernel methods. Moreover, such aExpand
Generalized Partially Linear Single-Index Models
Abstract The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these modelsExpand
Nonconcave penalized likelihood with a diverging number of parameters
A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables.Expand
Profile likelihood inferences on semiparametric varying-coefficient partially linear models
Varying-coefficient partially linear models are frequently used in statistical modelling, but their estimation and inference have not been systematically studied. This paper proposes a profileExpand
Generalized likelihood ratio statistics and Wilks phenomenon
Likelihood ratio theory has had tremendous success in parametric inference, due to the fundamental theory of Wilks. Yet, there is no general applicable approach for nonparametric inferences based onExpand
Efficient Estimation of Conditional Variance Functions in Stochastic Regression
Conditional heteroscedasticity has been often used in modelling and understanding the variability of statistical data. Under a general setup which includes the nonlinear time series model as aExpand