Department of Economics and Business Economics

Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso

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Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso. / Caner, Mehmet; Kock, Anders Bredahl.

In: Journal of Econometrics, Vol. 203, No. 1, 2018, p. 143-168.

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@article{104e03c042f043c4b154b6f71c6dbbae,
title = "Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso",
abstract = "In this paper we consider the conservative Lasso which we argue penalizes more correctly than the Lasso and show how it may be desparsified in the sense of van de Geer et al. (2014) in order to construct asymptotically honest (uniform) confidence bands. In particular, we develop an oracle inequality for the conservative Lasso only assuming the existence of a certain number of moments. This is done by means of the Marcinkiewicz–Zygmund inequality. We allow for heteroskedastic non-subgaussian error terms and covariates. Next, we desparsify the conservative Lasso estimator and derive the asymptotic distribution of tests involving an increasing number of parameters. Our simulations reveal that the desparsified conservative Lasso estimates the parameters more precisely than the desparsified Lasso, has better size properties and produces confidence bands with superior coverage rates.",
keywords = "Confidence intervals, Conservative Lasso, High-dimensional data, Honest inference, INFERENCE, INTERVALS, MODELS, NONCONCAVE PENALIZED LIKELIHOOD, REGRESSION, Tests, Uniform inference, VARIABLE SELECTION",
author = "Mehmet Caner and Kock, {Anders Bredahl}",
year = "2018",
doi = "10.1016/j.jeconom.2017.11.005",
language = "English",
volume = "203",
pages = "143--168",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "1",

}

RIS

TY - JOUR

T1 - Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso

AU - Caner, Mehmet

AU - Kock, Anders Bredahl

PY - 2018

Y1 - 2018

N2 - In this paper we consider the conservative Lasso which we argue penalizes more correctly than the Lasso and show how it may be desparsified in the sense of van de Geer et al. (2014) in order to construct asymptotically honest (uniform) confidence bands. In particular, we develop an oracle inequality for the conservative Lasso only assuming the existence of a certain number of moments. This is done by means of the Marcinkiewicz–Zygmund inequality. We allow for heteroskedastic non-subgaussian error terms and covariates. Next, we desparsify the conservative Lasso estimator and derive the asymptotic distribution of tests involving an increasing number of parameters. Our simulations reveal that the desparsified conservative Lasso estimates the parameters more precisely than the desparsified Lasso, has better size properties and produces confidence bands with superior coverage rates.

AB - In this paper we consider the conservative Lasso which we argue penalizes more correctly than the Lasso and show how it may be desparsified in the sense of van de Geer et al. (2014) in order to construct asymptotically honest (uniform) confidence bands. In particular, we develop an oracle inequality for the conservative Lasso only assuming the existence of a certain number of moments. This is done by means of the Marcinkiewicz–Zygmund inequality. We allow for heteroskedastic non-subgaussian error terms and covariates. Next, we desparsify the conservative Lasso estimator and derive the asymptotic distribution of tests involving an increasing number of parameters. Our simulations reveal that the desparsified conservative Lasso estimates the parameters more precisely than the desparsified Lasso, has better size properties and produces confidence bands with superior coverage rates.

KW - Confidence intervals

KW - Conservative Lasso

KW - High-dimensional data

KW - Honest inference

KW - INFERENCE

KW - INTERVALS

KW - MODELS

KW - NONCONCAVE PENALIZED LIKELIHOOD

KW - REGRESSION

KW - Tests

KW - Uniform inference

KW - VARIABLE SELECTION

UR - http://www.scopus.com/inward/record.url?scp=85039458857&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2017.11.005

DO - 10.1016/j.jeconom.2017.11.005

M3 - Journal article

AN - SCOPUS:85039458857

VL - 203

SP - 143

EP - 168

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1

ER -