Performance bounds for parameter estimates of high-dimensional linear models with correlated errors
By Wei Biao Wu, Ying Nian Wu. 2016
120 citations recorded by the source corpus.
: This paper develops a systematic theory for high-dimensional linear models with dependent errors and/or dependent covariates. To study properties of estimates of the regression parameters, we adopt the framework of functional dependence measures ([43]). For the covariates two schemes are addressed: the random design and the deterministic design. For the former we apply the constrained (cid:2) 1 minimization approach, while for the latter the Lasso estimation procedure is used. We provide a detailed characterization on how the error rates of the estimates depend on the moment conditions that control the tail behaviors, the dependencies of the underlying processes that generate the errors and the covariates, the dimension and the sample size. Our theory substantially extends earlier ones by allowing dependent and/or heavy-tailed errors and the covariates. As our main tools, we derive exponential tail probability inequalities for dependent sub-Gaussian errors and Nagaev-type inequalities for dependent non-sub-Gaussian errors that arise from linear or non-linear processes.
Subfields: Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/b03f5f68c1307d5cdfef1252266a217808247dc2
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Citations in the corpus
- Machine Learning Advances for Time Series Forecasting (2020, methodology): “Wu and Wu (2016) derive oracle bounds for the LASSO on regression with fixed design and weak dependent innovations, in a sense of Wu (2005), whereas Han and Tsay (2020) show model selection consistency for linear regression with random design and weak sparsity 6 under serially dependent errors and…”