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Influence Diagnostics in Possibly Asymmetric Circular-Linear Multivariate Regression Models

Author

Listed:
  • S. Liu

    (University of Canberra)

  • T. Ma

    (Southwestern University of Finance and Economics)

  • A. SenGupta

    (Indian Statistical Institute)

  • K. Shimizu

    (The Institute of Statistical Mathematics)

  • M.-Z. Wang

    (The Institute of Statistical Mathematics)

Abstract

Distributional studies and regression models have played important roles in statistical analysis of circular data. Asymmetric circular-linear multivariate regression models (SenGupta and Ugwuowo Environ. Ecol. Stat. 13(3), 299–309 2006) are motivated by and applied to predict some environmental characteristics based on both circular and linear predictors. In this paper, we consider a likelihood approach (Cook J. R. Stat. Soc. Ser. B Stat Methodol. 48(2), 133–169 1986) to study influence diagnostic analysis for these models, using the maximum likelihood estimation and influence diagnostics methods. The observed information matrices and normal curvatures are derived. Simulated and real data examples are then provided to illustrate our approach and establish the utility of our results.

Suggested Citation

  • S. Liu & T. Ma & A. SenGupta & K. Shimizu & M.-Z. Wang, 2017. "Influence Diagnostics in Possibly Asymmetric Circular-Linear Multivariate Regression Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-93, May.
    • Handle: RePEc:spr:sankhb:v:79:y:2017:i:1:d:10.1007_s13571-016-0116-8
    DOI: 10.1007/s13571-016-0116-8
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    References listed on IDEAS

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    9. Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.
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    Cited by:

    1. Xiaoping Zhan & Tiefeng Ma & Shuangzhe Liu & Kunio Shimizu, 2018. "Markov-Switching Linked Autoregressive Model for Non-continuous Wind Direction Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(3), pages 410-425, September.
    2. Andrade, Ana C.C. & Pereira, Gustavo H.A. & Artes, Rinaldo, 2023. "The circular quantile residual," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    3. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Yonghui Liu & Guohua Mao & Víctor Leiva & Shuangzhe Liu & Alejandra Tapia, 2020. "Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    5. Olga Lingaitienė & Aurelija Burinskienė, 2021. "Core Elements towards Circularity: Evidence from the European Countries," Sustainability, MDPI, vol. 13(16), pages 1-16, August.

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