Asymptotically Honest Confidence Regions for High Dimensional Parameters by the Desparsified Conservative Lasso

By Mehmet Caner, Anders Bredahl Kock. 2014

74 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1c9b0bd09cbd955aa50163c9e6f6842bcc730964

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Citations in the corpus

CONSISTENT AND CONSERVATIVE MODEL SELECTION WITH THE ADAPTIVE LASSO IN STATIONARY AND NONSTATIONARY AUTOREGRESSIONS (2015, methodology): “…research include developing procedures for inference in high-dimensional time series models (where the number of parameters is more numerous than the number of observations) a la the desparsified Lasso of van de Geer et al. (2014) or the depsarsified conservative Lasso of Caner and Kock (2014).”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, background): “…Belloni et al. (2012), Belloni et al. (2014c), Caner and Zhang (2014), Belloni et al. (2016), Kock (2016a), Kock (2016b), Callot et al. (2017), Caner and Kock (2018); see Belloni et al. (2014a) for a review), the sparsity assumption was used to select among a large number of potential…”
A Nodewise Regression Approach to Estimating Large Portfolios (2016, methodology): “We discuss this point further in Section 2.3. van de Geer et al. (2014) and Caner and Kock (2018) used nodewise regression to build asymptotically honest confidence intervals for high-dimensional parameter vectors.”