Joint conditional quantiles inference of multivariate response regression model with VAR(q) error and its application in evaluating energy efficiency

Yuzhu Tian, Xiaoyu Niu, Yue Wang, Maozai Tian () and Chunho Wu
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Yuzhu Tian: Northwest Normal University
Xiaoyu Niu: Lanzhou University
Yue Wang: The Education University of Hong Kong
Maozai Tian: Renmin University of China
Chunho Wu: The Hang Seng University of Hong Kong

Statistical Papers, 2025, vol. 66, issue 6, No 3, 28 pages

Abstract: Abstract This paper presents the joint parameters inference of conditional quantiles for a multivariate response linear regression model with a vector autoregressive (VAR) error using the expectation-maximization (EM) algorithm. Because the error follows a VAR model, the proposed approach accounts for the associations among multivariate responses and how the relationships between responses and explanatory variables vary across different quantiles of the marginal conditional distribution of responses. To facilitate likelihood-based inference using the EM algorithm, a multivariate asymmetric Laplace (MAL) distribution is forced on the independent errors of the model, thereby allowing the construction of an equivalently joint quantile model. Meanwhile, a location-scale mixture representation of the MAL distribution is employed to simplify the model’s working likelihood structure. Last, we present simulation studies and the analysis of real data for concerning on energy efficiency evaluation in order to illustrate the proposed modeling approach’s effectiveness.

Keywords: VAR error; Multivariate response regression; MAL distribution; Joint quantile regression (QR) inference; EM algorithm; Energy efficiency (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01734-6

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