Adaptive efficient sparse estimator achieving oracle properties

In this paper, we consider variable selection in rank regression models for longitudinal data. To obtain both robustness and effective selection of important covariates, we propose incorporating shrinkage by adaptive lasso or SCAD in the Wilcoxon dispersion function and establishing the oracle properties of the new method. The new method can be conveniently implemented with the statistical software R. The performance of the proposed method is demonstrated via simulation studies. Finally, two datasets are analyzed for illustration. Some interesting findings are reported and discussed.

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Estimation for Varying Coefficient Models with Hierarchical Structure

Mathematics ◽

10.3390/math9020132 ◽

2021 ◽

Vol 9 (2) ◽

pp. 132

Author(s):

Feng Li ◽

Yajie Li ◽

Sanying Feng

Keyword(s):

Variable Selection ◽

Hierarchical Structure ◽

Kernel Method ◽

Real Data ◽

Unknown Coefficient ◽

Nonparametric Model ◽

Finite Sample ◽

Oracle Properties ◽

Varying Coefficient ◽

The Hierarchical Structure

The varying coefficient (VC) model is a generalization of ordinary linear model, which can not only retain strong interpretability but also has the flexibility of the nonparametric model. In this paper, we investigate a VC model with hierarchical structure. A unified variable selection method for VC model is proposed, which can simultaneously select the nonzero effects and estimate the unknown coefficient functions. Meanwhile, the selected model enforces the hierarchical structure, that is, interaction terms can be selected into the model only if the corresponding main effects are in the model. The kernel method is employed to estimate the varying coefficient functions, and a combined overlapped group Lasso regularization is introduced to implement variable selection to keep the hierarchical structure. It is proved that the proposed penalty estimators have oracle properties, that is, the coefficients are estimated as well as if the true model were known in advance. Simulation studies and a real data analysis are carried out to examine the performance of the proposed method in finite sample case.

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PSNA: A pathwise semismooth Newton algorithm for sparse recovery with optimal local convergence and oracle properties

Signal Processing ◽

10.1016/j.sigpro.2021.108432 ◽

2021 ◽

pp. 108432

Author(s):

Jian Huang ◽

Yuling Jiao ◽

Xiliang Lu ◽

Yueyong Shi ◽

Qinglong Yang ◽

...

Keyword(s):

Local Convergence ◽

Sparse Recovery ◽

Oracle Properties ◽

Newton Algorithm ◽

Semismooth Newton

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Bootstrap inference for penalized GMM estimators with oracle properties

Econometric Reviews ◽

10.1080/07474938.2019.1630076 ◽

2019 ◽

Vol 39 (4) ◽

pp. 362-372

Author(s):

Lorenzo Camponovo

Keyword(s):

Oracle Properties ◽

Bootstrap Inference

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ADAPTIVE GMM SHRINKAGE ESTIMATION WITH CONSISTENT MOMENT SELECTION

Econometric Theory ◽

10.1017/s0266466612000783 ◽

2013 ◽

Vol 29 (5) ◽

pp. 857-904 ◽

Cited By ~ 39

Author(s):

Zhipeng Liao

Keyword(s):

Political Economy ◽

Labor Supply ◽

Generalized Method Of Moments ◽

Finite Sample ◽

Unknown Parameters ◽

Moment Conditions ◽

Oracle Properties ◽

Moment Selection ◽

Finite Sample Properties ◽

Shrinkage Method

This paper proposes a generalized method of moments (GMM) shrinkage method to efficiently estimate the unknown parameters θo identified by some moment restrictions, when there is another set of possibly misspecified moment conditions. We show that our method enjoys oracle-like properties; i.e., it consistently selects the correct moment conditions in the second set and at the same time, its estimator is as efficient as the GMM estimator based on all correct moment conditions. For empirical implementation, we provide a simple data-driven procedure for selecting the tuning parameters of the penalty function. We also establish oracle properties of the GMM shrinkage method in the practically important scenario where the moment conditions in the first set fail to strongly identify θo. The simulation results show that the method works well in terms of correct moment selection and the finite sample properties of its estimators. As an empirical illustration, we apply our method to estimate the life-cycle labor supply equation studied in MaCurdy (1981, Journal of Political Economy 89(6), 1059–1085) and Altonji (1986, Journal of Political Economy 94(3), 176–215). Our empirical findings support the validity of the instrumental variables used in both papers and confirm that wage is an endogenous variable in the labor supply equation.

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