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Partial Consistency with Sparse Incidental Parameters.

Jianqing Fan1, Runlong Tang2, Xiaofeng Shi1

  • 1Princeton University.

Statistica Sinica
|October 15, 2019
PubMed
Summary
This summary is machine-generated.

This study applies penalized estimation to linear regression with structural and sparse incidental parameters. Structural parameters are consistently estimated, while incidental parameters show partial selection consistency, not full consistency.

Keywords:
Confidence IntervalsOracle PropertyPartial ConsistencyPenalized EstimationSparse Incidental ParametersStructural ParametersTwo-Step Estimation

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Penalized estimation is crucial for high-dimensional data.
  • Existing methods primarily focus on models with only structural parameters.

Purpose of the Study:

  • To apply penalized estimation to linear regression with both structural and high-dimensional sparse incidental parameters.
  • To analyze the estimation properties for both parameter types.

Main Methods:

  • Applying the penalization principle to a linear regression model.
  • Deriving consistency and asymptotic normality for structural parameter estimators.
  • Investigating the properties of penalized estimators for incidental parameters.

Main Results:

  • Structural parameter estimators exhibit consistency and asymptotic normality (oracle property).
  • Incidental parameter estimators demonstrate partial selection consistency but not full consistency.
  • An alternative two-step penalized estimator is proposed for structural parameters.

Conclusions:

  • The study highlights a novel partial consistency phenomenon in high-dimensional penalized regression.
  • The findings offer insights into the behavior of penalized estimators with both structural and incidental parameters.
  • Methods are extended to diverging dimensions, with a data-driven regularization parameter selection approach provided.