IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i5d10.1007_s00362-025-01737-3.html
   My bibliography  Save this article

Mean regression model for Type I generalized logistic distribution with a QLB algorithm

Author

Listed:
  • Xun-Jian Li

    (The Hong Kong Polytechnic University)

  • Jiajuan Liang

    (Hong Kong Baptist University)

  • Guo-Liang Tian

    (Southern University of Science and Technology)

  • Man-Lai Tang

    (University of Hertfordshire)

  • Jianhua Shi

    (Minnan Normal University)

Abstract

Skewed data often appear in actuarial, biological, medical studies, clinical trials, industrial and engineering fields. To model such skewed data, a lot of skew distributions including skew normal/t/logistic have been proposed to investigate the relationship between the response variable and a set of explanatory variables. However, to our best knowledge, there exists few mean regression model based on skew distributions. This paper applies the Type I generalized logistic ( $$\text {GL}^{\text{(I)}}$$ ) distribution to construct a mean regression model for fitting skewed data. First, we reparameterize the shape, location and scale parameters to ensure the existence of maximum likelihood estimators (MLEs) of parameters even for the embedded model problem. Next, we develop a new quadratic lower bound (QLB) algorithm with monotone convergence to calculate MLEs of parameters, which has been proved to be computationally efficient even for the high-dimensional vector of covariates with correlated components in simulations. A real data set is analyzed to illustrate the proposed methods.

Suggested Citation

  • Xun-Jian Li & Jiajuan Liang & Guo-Liang Tian & Man-Lai Tang & Jianhua Shi, 2025. "Mean regression model for Type I generalized logistic distribution with a QLB algorithm," Statistical Papers, Springer, vol. 66(5), pages 1-42, August.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:5:d:10.1007_s00362-025-01737-3
    DOI: 10.1007/s00362-025-01737-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-025-01737-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-025-01737-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Dankmar Böhning & Bruce Lindsay, 1988. "Monotonicity of quadratic-approximation algorithms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 641-663, December.
    2. Lan Wang & Bo Peng & Jelena Bradic & Runze Li & Yunan Wu, 2020. "A Tuning-free Robust and Efficient Approach to High-dimensional Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1700-1714, December.
    3. Behboodian, J. & Jamalizadeh, A. & Balakrishnan, N., 2006. "A new class of skew-Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1488-1493, August.
    4. Saralees Nadarajah, 2009. "The skew logistic distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(2), pages 187-203, June.
    5. Jeffrey S. Simonoff & Chih‐Ling Tsai, 1994. "Use of Modified Profile Likelihood for Improved Tests of Constancy of Variance in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 357-370, June.
    6. Lan Wang & Bo Peng & Jelena Bradic & Runze Li & Yunan Wu, 2020. "Rejoinder to “A Tuning-Free Robust and Efficient Approach to High-Dimensional Regression”," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1726-1729, December.
    7. Jianqing Fan & Cong Ma & Kaizheng Wang, 2020. "Comment on “A Tuning-Free Robust and Efficient Approach to High-Dimensional Regression”," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1720-1725, December.
    8. Turan Bali, 2007. "Modeling the dynamics of interest rate volatility with skewed fat-tailed distributions," Annals of Operations Research, Springer, vol. 151(1), pages 151-178, April.
    9. Cantoni, Eva & Ronchetti, Elvezio, 2006. "A robust approach for skewed and heavy-tailed outcomes in the analysis of health care expenditures," Journal of Health Economics, Elsevier, vol. 25(2), pages 198-213, March.
    10. Zelterman, D., 1987. "Parameter estimation in the generalized logistic distribution," Computational Statistics & Data Analysis, Elsevier, vol. 5(3), pages 177-184.
    11. Xiudi Li & Ali Shojaie, 2020. "Discussion of “A Tuning-Free Robust and Efficient Approach to High-Dimensional Regression”," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1717-1719, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.
    2. Jack Jewson & David Rossell, 2022. "General Bayesian loss function selection and the use of improper models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1640-1665, November.
    3. Xinyu Fu & Mian Huang & Weixin Yao, 2024. "Semiparametric efficient estimation in high‐dimensional partial linear regression models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1259-1287, September.
    4. Mingyang Ren & Sanguo Zhang & Junhui Wang, 2023. "Consistent estimation of the number of communities via regularized network embedding," Biometrics, The International Biometric Society, vol. 79(3), pages 2404-2416, September.
    5. Yu, Ke & Luo, Shan, 2024. "Rank-based sequential feature selection for high-dimensional accelerated failure time models with main and interaction effects," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    6. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.
    7. Dong, Wei & Xu, Chen & Xie, Jinhan & Tang, Niansheng, 2024. "Tuning-free sparse clustering via alternating hard-thresholding," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    8. Courbage, Christophe & Rey, Béatrice, 2012. "Priority setting in health care and higher order degree change in risk," Journal of Health Economics, Elsevier, vol. 31(3), pages 484-489.
    9. Roussille, Nina & Scuderi, Benjamin, 2023. "Bidding for Talent: A Test of Conduct in a High-Wage Labor Market," IZA Discussion Papers 16352, Institute of Labor Economics (IZA).
    10. Wang, Fa, 2022. "Maximum likelihood estimation and inference for high dimensional generalized factor models with application to factor-augmented regressions," Journal of Econometrics, Elsevier, vol. 229(1), pages 180-200.
    11. Utkarsh J. Dang & Michael P.B. Gallaugher & Ryan P. Browne & Paul D. McNicholas, 2023. "Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 145-167, April.
    12. Zhu, Zhongyi & Fung, Wing K., 2004. "Variance component testing in semiparametric mixed models," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 107-118, October.
    13. Mahdi Rasekhi & G. G. Hamedani & Rahim Chinipardaz, 2017. "A flexible extension of skew generalized normal distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 87-107, April.
    14. Tian, Guo-Liang & Tang, Man-Lai & Liu, Chunling, 2012. "Accelerating the quadratic lower-bound algorithm via optimizing the shrinkage parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 255-265.
    15. Wong, Heung & Liu, Feng & Chen, Min & Ip, Wai Cheung, 2009. "Empirical likelihood based diagnostics for heteroscedasticity in partial linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3466-3477, July.
    16. Shakhatreh, M.K., 2012. "A two-parameter of weighted exponential distributions," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 252-261.
    17. Carsten Colombier, 2018. "Population ageing in healthcare – a minor issue? Evidence from Switzerland," Applied Economics, Taylor & Francis Journals, vol. 50(15), pages 1746-1760, March.
    18. Chun-Zheng Cao & Jin-Guan Lin & Li-Xing Zhu, 2010. "Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors," Statistical Papers, Springer, vol. 51(4), pages 813-836, December.
    19. Bohning, Dankmar, 1999. "The lower bound method in probit regression," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 13-17, March.
    20. Manos Matsaganis & Theodore Mitrakos & Panos Tsakloglou, 2008. "Modelling Household Expenditure on Health Care in Greece," Working Papers 68, Bank of Greece.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:66:y:2025:i:5:d:10.1007_s00362-025-01737-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.