Arbeitspapier

Valid post-selection inference in high-dimensional approximately sparse quantile regression models

This work proposes new inference methods for the estimation of a regression coefficient of interest in quantile regression models. We consider high-dimensional models where the number of regressors potentially exceeds the sample size but a subset of them suffice to construct a reasonable approximation of the unknown quantile regression function in the model. The proposed methods are protected against moderate model selection mistakes, which are often inevitable in the approximately sparse model considered here. The methods construct (implicitly or explicitly) an optimal instrument as a residual from a density-weighted projection of the regressor of interest on other regressors. Under regularity conditions, the proposed estimators of the quantile regression coefficient are asymptotically root-n normal, with variance equal to the semi-parametric efficiency bound of the partially linear quantile regression model. In addition, the performance of the technique is illustrated through Monte-carlo experiments and an empirical example, dealing with risk factors in childhood malnutrition. The numerical results confirm the theoretical findings that the proposed methods should outperform the naive post-model selection methods in non-parametric settings. Moreover, the empirical results demonstrate soundness of the proposed methods.

Language
Englisch

Bibliographic citation
Series: cemmap working paper ; No. CWP53/14

Classification
Wirtschaft

Event
Geistige Schöpfung
(who)
Belloni, Alexandre
Chernozhukov, Victor
Kato, Kengo
Event
Veröffentlichung
(who)
Centre for Microdata Methods and Practice (cemmap)
(where)
London
(when)
2014

DOI
doi:10.1920/wp.cem.2014.5314
Handle
Last update
10.03.2025, 11:42 AM CET

Data provider

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Object type

  • Arbeitspapier

Associated

  • Belloni, Alexandre
  • Chernozhukov, Victor
  • Kato, Kengo
  • Centre for Microdata Methods and Practice (cemmap)

Time of origin

  • 2014

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