scholarly journals Oracle inequalities for high-dimensional prediction

Bernoulli ◽  
2019 ◽  
Vol 25 (2) ◽  
pp. 1225-1255 ◽  
Author(s):  
Johannes Lederer ◽  
Lu Yu ◽  
Irina Gaynanova
Keyword(s):  
High Dimensional ◽  
Oracle Inequalities

scholarly journals UNIFORM INFERENCE IN HIGH-DIMENSIONAL DYNAMIC PANEL DATA MODELS WITH APPROXIMATELY SPARSE FIXED EFFECTS

2018 ◽  
Vol 35 (2) ◽  
pp. 295-359 ◽  
Author(s):  
Anders Bredahl Kock ◽  
Haihan Tang
Keyword(s):  
Panel Data ◽  
Fixed Effects ◽  
Dynamic Panel Data ◽  
High Dimensional ◽  
Conditional Heteroskedasticity ◽  
Panel Data Models ◽  
Parameter Vector ◽  
Dynamic Panel ◽  
Oracle Inequalities ◽  
Dynamic Panel Data Models

We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities are derived for the fixed effects. Next, we show how one can conduct uniformly valid inference on the parameters of the model and construct a uniformly valid estimator of the asymptotic covariance matrix which is robust to conditional heteroskedasticity in the error terms. Allowing for conditional heteroskedasticity is important in dynamic models as the conditional error variance may be nonconstant over time and depend on the covariates. Furthermore, our procedure allows for inference on high-dimensional subsets of the parameter vector of an increasing cardinality. We show that the confidence bands resulting from our procedure are asymptotically honest and contract at the optimal rate. This rate is different for the fixed effects than for the remaining parts of the parameter vector.

scholarly journals Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yijun Xiao ◽  
Ting Yan ◽  
Huiming Zhang ◽  
Yuanyuan Zhang
Keyword(s):  
Estimation Error ◽  
Group Lasso ◽  
High Dimensional ◽  
Group Sparsity ◽  
Oracle Inequalities ◽  
Cox Models ◽  
Special Cases ◽  
Coefficient Vector ◽  
General Norm ◽  
Time Dependent Covariates

AbstractWe study the nonasymptotic properties of a general norm penalized estimator, which include Lasso, weighted Lasso, and group Lasso as special cases, for sparse high-dimensional misspecified Cox models with time-dependent covariates. Under suitable conditions on the true regression coefficients and random covariates, we provide oracle inequalities for prediction and estimation error based on the group sparsity of the true coefficient vector. The nonasymptotic oracle inequalities show that the penalized estimator has good sparse approximation of the true model and enables to select a few meaningful structure variables among the set of features.

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