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Burak KL, Kashlak AB. Nonparametric confidence regions via the analytic wild bootstrap. CAN J STAT 2022. [DOI: 10.1002/cjs.11687] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Katherine L. Burak
- Department of Mathematical and Statistical Sciences University of Alberta Edmonton AB Canada T6G 2G1
| | - Adam B. Kashlak
- Department of Mathematical and Statistical Sciences University of Alberta Edmonton AB Canada T6G 2G1
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Xu Q, Ding X, Jiang C, Yu K, Shi L. An elastic-net penalized expectile regression with applications. J Appl Stat 2021; 48:2205-2230. [DOI: 10.1080/02664763.2020.1787355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Q.F. Xu
- School of Management, Hefei University of Technology, Hefei, People's Republic of China
- Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, People's Republic of China
| | - X.H. Ding
- School of Management, Hefei University of Technology, Hefei, People's Republic of China
| | - C.X. Jiang
- School of Management, Hefei University of Technology, Hefei, People's Republic of China
| | - K.M. Yu
- Department of Mathematics, Brunel University London, Uxbridge, UK
| | - L. Shi
- School of Computer Science and Technology, Huaibei Normal University, Huaibei, People's Republic of China
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Flórez AJ, Keilegom IV, Molenberghs G, Verhasselt A. Quantile regression for longitudinal data via the multivariate generalized hyperbolic distribution. STAT MODEL 2021. [DOI: 10.1177/1471082x211015454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
While extensive research has been devoted to univariate quantile regression, this is considerably less the case for the multivariate (longitudinal) version, even though there are many potential applications, such as the joint examination of growth curves for two or more growth characteristics, such as body weight and length in infants. Quantile functions are easier to interpret for a population of curves than mean functions. While the connection between multivariate quantiles and the multivariate asymmetric Laplace distribution is known, it is less well known that its use for maximum likelihood estimation poses mathematical as well as computational challenges. Therefore, we study a broader family of multivariate generalized hyperbolic distributions, of which the multivariate asymmetric Laplace distribution is a limiting case. We offer an asymptotic treatment. Simulations and a data example supplement the modelling and theoretical considerations.
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Affiliation(s)
- Alvaro J. Flórez
- DSI, I-BioStat, Universiteit Hasselt, Belgium and School of Statistics, Universidad del Valle, Colombia
| | | | - Geert Molenberghs
- DSI, I-BioStat, Universiteit Hasselt, Belgium and I-BioStat, KU Leuven, Belgium
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