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

2014/10/15 by Mehmet Caner, Anders Kock, Caner, Mehmet +1
Mathematics · #Advanced Causal Inference Techniques #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1410.4208

openalex publication_date 2014/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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