A sparse approach for high-dimensional data with heavy-tailed noise

Bibliographic Data

ID15067274
AuthorsYafen Ye (0000-0001-6000-8635, Zhejiang University of Technology), Yuanhai Shao (Management School, Hainan University, Haikou, P.R. China), Yuan-Hai Shao (0000-0002-1628-6133, Hainan University), Chunna Li (0000-0003-3476-1505, Management School, Hainan University, Haikou, P.R. China), Chun‐Na Li (0000-0001-7033-0089, Hainan University, corresponding author)
Year2022
Volume35
Issue1
Pages2764-2780
Publication date2022-12-31
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueEconomic Research-Ekonomska Istraživanja (JOURNAL)
Journal identifiersISSN: 1331-677X • E-ISSN: 1848-9664
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/1331677x.2021.1978306
OpenAlexW3201153711
LanguageEN
References cited42

High-dimensional data have commonly emerged in diverse fields, such as economics, finance, genetics, medicine, machine learning, and so on. In this paper, we consider the sparse quantile regression problem of high-dimensional data with heavy-tailed noise, especially when the number of regressors is much larger than the sample size. We bring the spirit of -norm support vector regression into quantile regression and propose a robust -norm support vector quantile regression for high-dimensional data with heavy-tailed noise. The proposed method achieves robustness against heavy-tailed noise due to its use of the pinball loss function. Furthermore, -norm support vector quantile regression ensures that the most representative variables are selected automatically by using a sparse parameter. We use a simulation study to test the variable selection performance of -norm support vector quantile regression, where the number of explanatory variables greatly exceeds the sample size. The simulation study confirms that -norm support vector quantile regression is not only robust against heavy-tailed noise but also selects representative variables. We further apply the proposed method to solve the variable selection problem of index construction, which also confirms the robustness and sparseness of -norm support vector quantile regression

Econometrics · Feature selection · Linear regression · Quantile · Quantile regression · Regression analysis · Sample size determination · Statistics · Support vector machine · Bayesian Methods and Mixture Models · Computer Science · Gene expression and cancer classification · Mathematics · Statistical Methods and Inference · Artificial Intelligence