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Expectile regression for analyzing heteroscedasticity in high dimension

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  • Zhao, Jun
  • Chen, Yingyu
  • Zhang, Yi

Abstract

High-dimensional data often display heteroscedasticity and this feature has attracted a lot of attention and discussion. In this paper, we propose regularized expectile regression with SCAD penalty for analyzing heteroscedasticity in high dimension when the error has finite moments. Since the corresponding optimization problem is nonconvex due to the SCAD penalty, we adopt the CCCP (coupling of the concave and convex procedure) algorithm to solve this problem. Under some regular conditions, we can prove that with probability tending to one, the proposed algorithm converges to the oracle estimator after several iterations. We should address that the higher order moment the error has, the higher dimension cardinality our procedure can handle with. If the error follows gaussian or sub-gaussian distribution, our method can be extended to deal with ultra high-dimensional data. Furthermore, by taking different expectile weight level α, we are able to detect heteroscedasticity and explore the entire conditional distribution of the response variable given all the covariates. We investigate the performances of our proposed method through Monte Carlo simulation study and real application and the numerical results show that the resulting estimator by our algorithm enjoys good performance and demonstrate the usefulness of our proposed method to analyze heteroscedasticity.

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  • Zhao, Jun & Chen, Yingyu & Zhang, Yi, 2018. "Expectile regression for analyzing heteroscedasticity in high dimension," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 304-311.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:304-311
    DOI: 10.1016/j.spl.2018.02.006
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    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-396, June.
    3. Jianqing Fan & Quefeng Li & Yuyan Wang, 2017. "Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 247-265, January.
    4. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    5. Schnabel, Sabine K. & Eilers, Paul H.C., 2009. "Optimal expectile smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4168-4177, October.
    6. Sobotka, Fabian & Kneib, Thomas, 2012. "Geoadditive expectile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 755-767.
    7. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    8. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
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    Cited by:

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    3. Jun Zhao & Guan’ao Yan & Yi Zhang, 2022. "Robust estimation and shrinkage in ultrahigh dimensional expectile regression with heavy tails and variance heterogeneity," Statistical Papers, Springer, vol. 63(1), pages 1-28, February.
    4. Gabriela Ciuperca, 2022. "Real-time detection of a change-point in a linear expectile model," Statistical Papers, Springer, vol. 63(4), pages 1323-1367, August.
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    6. Gao, Suhao & Yu, Zhen, 2023. "Parametric expectile regression and its application for premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 242-256.
    7. Mustapha Rachdi & Ali Laksaci & Noriah M. Al-Kandari, 2022. "Expectile regression for spatial functional data analysis (sFDA)," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 627-655, July.

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