IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v188y2022ics0047259x21000798.html
   My bibliography  Save this article

Conditional specification of statistical models: Classical models, new developments and challenges

Author

Listed:
  • Arnold, Barry C.
  • Sarabia, José María

Abstract

In a bivariate distribution, it is sometimes easier to visualize conditional distributions of experimental variables rather than the joint distribution. In this sense, the subject of conditional specification of distributions has become an active field of research in recent years as part of multivariate analysis. In this article we summarize some of the main aspects of models with conditional specification. In addition, we highlight the most relevant aspects of these models and establish some challenges that we will face in the coming years.

Suggested Citation

  • Arnold, Barry C. & Sarabia, José María, 2022. "Conditional specification of statistical models: Classical models, new developments and challenges," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21000798
    DOI: 10.1016/j.jmva.2021.104801
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21000798
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104801?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Sarabia, José María & Guillén, Montserrat, 2008. "Joint modelling of the total amount and the number of claims by conditionals," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 466-473, December.
    2. José Sarabia & Enrique Castillo & Marta Pascual & María Sarabia, 2007. "Bivariate income distributions with lognormal conditionals," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 371-383, December.
    3. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    4. J. Navarro & M. Esna-Ashari & M. Asadi & J. Sarabia, 2015. "Bivariate distributions with conditionals satisfying the proportional generalized odds rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 691-709, August.
    5. Kmietowicz, Z W, 1984. "The Bivariate Lognormal Model for the Distribution of Household Size and Income," The Manchester School of Economic & Social Studies, University of Manchester, vol. 52(2), pages 196-210, June.
    6. Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
    7. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    8. Sarabia, José María & Gómez-Déniz, Emilio & Vázquez-Polo, Francisco J., 2004. "On the Use of Conditional Specification Models in Claim Count Distributions: an Application to Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 85-98, May.
    9. Fry, Renée & Martin, Vance L. & Tang, Chrismin, 2010. "A New Class of Tests of Contagion With Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 423-437.
    10. Arnold, Barry C., 1987. "Bivariate distributions with pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 263-266, June.
    11. Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose María, 1993. "Multivariate distributions with generalized Pareto conditionals," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 361-368, August.
    12. Navarro, Jorge & Sarabia, José María, 2013. "Reliability properties of bivariate conditional proportional hazard rate models," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 116-127.
    13. Kim, Sungsu & SenGupta, Ashis & Arnold, Barry C., 2016. "A multivariate circular distribution with applications to the protein structure prediction problem," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 374-382.
    14. Arnold, Barry C. & Castillo, Enrique & Sarabia, JoseMaria, 1998. "The use of conditionally conjugate priors in the study of ratios of gamma scale parameters," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 125-139, April.
    15. E. Castillo & J. Galambos, 1989. "Conditional distributions and the bivariate normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 209-214, December.
    16. Arnold, Barry C. & Castillo, Enrique & Sarabia, José María & González-Vega, Laureano, 2000. "Multiple modes in densities with normal conditionals," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 355-363, October.
    17. José María Sarabia & A. Vincent Raja & G. Asha, 2020. "Bivariate distributions with transmuted conditionals: Models and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(1), pages 221-242, January.
    18. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
    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. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    2. Gupta, Ramesh C., 2001. "Reliability Studies of Bivariate Distributions with Pareto Conditionals," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 214-225, February.
    3. Ramesh C. Gupta, 2006. "Reliability studies of bivariate distributions with Pearson type VII conditionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 239-251.
    4. Sarabia, José María & Gómez-Déniz, Emilio & Prieto, Faustino & Jordá, Vanesa, 2016. "Risk aggregation in multivariate dependent Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 154-163.
    5. Huang Yangxin & Chen Ren & Dagne Getachew, 2011. "Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-28, January.
    6. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    7. Phil D. Young & Joshua D. Patrick & John A. Ramey & Dean M. Young, 2020. "An Alternative Matrix Skew-Normal Random Matrix and Some Properties," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 28-49, February.
    8. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
    9. Young, Phil D. & Harvill, Jane L. & Young, Dean M., 2016. "A derivation of the multivariate singular skew-normal density function," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 40-45.
    10. Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.
    11. F. Kahrari & C. S. Ferreira & R. B. Arellano-Valle, 2019. "Skew-Normal-Cauchy Linear Mixed Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 185-202, December.
    12. Huang Yangxin & Chen Jiaqing & Yan Chunning, 2012. "Mixed-Effects Joint Models with Skew-Normal Distribution for HIV Dynamic Response with Missing and Mismeasured Time-Varying Covariate," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-30, November.
    13. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Zeller, Camila Borelli, 2014. "Multivariate measurement error models using finite mixtures of skew-Student t distributions," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 179-198.
    14. Ramesh Gupta, 2011. "Bivariate odds ratio and association measures," Statistical Papers, Springer, vol. 52(1), pages 125-138, February.
    15. Kim, Hyoung-Moon & Genton, Marc G., 2011. "Characteristic functions of scale mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1105-1117, August.
    16. Antonio Canale & Euloge Clovis Kenne Pagui & Bruno Scarpa, 2016. "Bayesian modeling of university first-year students' grades after placement test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 3015-3029, December.
    17. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    18. Vinh, Andrea & Griffiths, William E. & Chotikapanich, Duangkamon, 2010. "Bivariate income distributions for assessing inequality and poverty under dependent samples," Economic Modelling, Elsevier, vol. 27(6), pages 1473-1483, November.
    19. Lin, Tsung-I & McLachlan, Geoffrey J. & Lee, Sharon X., 2016. "Extending mixtures of factor models using the restricted multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 398-413.
    20. J. Navarro & M. Esna-Ashari & M. Asadi & J. Sarabia, 2015. "Bivariate distributions with conditionals satisfying the proportional generalized odds rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 691-709, August.

    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:eee:jmvana:v:188:y:2022:i:c:s0047259x21000798. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.