Arbeitspapier
Confidence bands for coefficients in high dimensional linear models with error-in-variables
We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to avoid non-vanishing biases in addition to handle the high dimensionality of the parameters. A recent growing literature has proposed various estimators that achieve good rates of convergence. Our main contribution complements this literature with the construction of simultaneous confidence regions for the parameters of interest in such high-dimensional linear models with error-in-variables. These confidence regions are based on the construction of moment conditions that have an additional orthogonality property with respect to nuisance parameters. We provide a construction that requires us to estimate an auxiliary high-dimensional linear model with error-in-variables for each component of interest. We use a multiplier bootstrap to compute critical values for simultaneous confidence intervals for a target subset of the components. We show its validity despite of possible (moderate) model selection mistakes, and allowing the number of target coefficients to be larger than the sample size. We apply and discuss the implications of our results to two examples and conduct Monte Carlo simulations to illustrate the performance of the proposed procedure for each variable whose coefficient is the target of inference.
- Language
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Englisch
- Bibliographic citation
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Series: cemmap working paper ; No. CWP22/17
- Classification
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Wirtschaft
- Subject
-
honest confidence regions
error-in-variables
high dimensional models
- Event
-
Geistige Schöpfung
- (who)
-
Belloni, Alexandre
Chernozhukov, Victor
Kaul, Abhishek
- Event
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Veröffentlichung
- (who)
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Centre for Microdata Methods and Practice (cemmap)
- (where)
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London
- (when)
-
2017
- DOI
-
doi:10.1920/wp.cem.2017.2217
- Handle
- Last update
-
10.03.2025, 11:41 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Arbeitspapier
Associated
- Belloni, Alexandre
- Chernozhukov, Victor
- Kaul, Abhishek
- Centre for Microdata Methods and Practice (cemmap)
Time of origin
- 2017
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