• Corpus ID: 237194774

Weak signal identification and inference in penalized likelihood models for categorical responses

  title={Weak signal identification and inference in penalized likelihood models for categorical responses},
  author={Yuexia Zhang and Peibei Shi and Zhongyi Zhu and Linbo Wang and Annie Qu},
Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid inference. Thus, identifying weak signals accurately and making valid inferences are crucial in penalized likelihood models. We develop a unified approach to identify weak signals and make inferences in penalized likelihood models, including the special case when… 

Figures from this paper



Weak signal identification and inference in penalized model selection

This paper proposes an identification procedure for weak signals in finite samples, and introduces a new two-step inferential method to construct better confidence intervals for the identified weak signals.

Weak Signals in High-Dimensional Logistic Regression Models

This work proposed post-selection improved estimation based on linear shrinkage, pretest, and James-Stein shrinkage strategies, which efficiently combine overfitted and underfitted ML estimators, which were severely affected by inappropriate variable selection.

Weak signals in high-dimension regression: detection, estimation and prediction.

This paper proposes a two-stage procedure, consisting of variable selection and post-selection estimation, and establishes asymptotic properties for the proposed method and shows that incorporating weak signals can improve estimation and prediction performance.

A Perturbation Method for Inference on Regularized Regression Estimates

This article proposes perturbation resampling-based procedures to approximate the distribution of a general class of penalized parameter estimates, justified by asymptotic theory, and provides a simple way to estimate the covariance matrix and confidence regions.

A Unified Theory of Confidence Regions and Testing for High-Dimensional Estimating Equations

A new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations is proposed, which is likelihood-free and provides valid inference for a broad class of highdimensional constrained estimating equation problems, which are not covered by existing methods.

Estimation and Accuracy After Model Selection

  • B. Efron
  • Mathematics
    Journal of the American Statistical Association
  • 2014
This work considers bootstrap methods for computing standard errors and confidence intervals that take model selection into account, also known as bootstrap smoothing, to tame the erratic discontinuities of selection-based estimators.

Model selection and estimation in regression with grouped variables

Summary.  We consider the problem of selecting grouped variables (factors) for accurate prediction in regression. Such a problem arises naturally in many practical situations with the multifactor

One-step Sparse Estimates in Nonconcave Penalized Likelihood Models.

A new unified algorithm based on the local linear approximation for maximizing the penalized likelihood for a broad class of concave penalty functions and shows that if the regularization parameter is appropriately chosen, the one-step LLA estimates enjoy the oracle properties with good initial estimators.

Confidence intervals for low dimensional parameters in high dimensional linear models

The method proposed turns the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients, which can be used to select variables after proper thresholding, and demonstrates the accuracy of the coverage probability and other desirable properties of the confidence intervals proposed.

Unified LASSO Estimation by Least Squares Approximation

If the adaptive LASSO penalty and a Bayes information criterion–type tuning parameter selector are used and the resulting LSA estimator can be as efficient as the oracle, the standard asymptotic theory can be established and the LARS algorithm can be applied.