Oracle inequalities for high-dimensional panel data models

Anders Kock

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we establish finite sample upper bounds on the estimation error of the Lasso under two different sets of conditions on the covariates as well as the error terms. Upper bounds on the estimation error of the unobserved heterogeneity are also provided under the assumption of sparsity. Next, we show that our upper bounds are essentially optimal in the sense that they can only be improved by multiplicative constants. These results are then used to show that the Lasso can be consistent in even very large models where the number of regressors increases at an exponential rate in the sample size. Conditions under which the Lasso does not discard any relevant variables asymptotically are also provided. In the second part of the paper we give lower bounds on the probability with which the adaptive Lasso selects the correct sparsity pattern in finite samples. These results are then used to give conditions under which the adaptive Lasso can detect the correct sparsity pattern asymptotically. We illustrate our finite sample results by simulations and apply the methods to search for covariates explaining growth in the G8 countries.

Keywords: Panel data; Lasso; Adaptive Lasso; Oracle inequality; Nonasymptotic bounds; High-dimensional models; Sparse models; Consistency; Variable selection; Asymptotic sign consistency. (search for similar items in EconPapers)
JEL-codes: C01 C13 C23 (search for similar items in EconPapers)
Pages: 37
Date: 2013-12-06
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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