IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i2d10.1007_s13171-022-00292-5.html
   My bibliography  Save this article

A Class of Multivariate Power Skew Symmetric Distributions: Properties and Inference for the Power-Parameter

Author

Listed:
  • R. N. Rattihalli

Abstract

Let SPd be the class of all multivariate sign and permutation invariant densities and SPD be the corresponding class of distribution functions. The class of all distributions corresponding to a positive power of the members of SPD is called the Power Skew Symmetric class of distributions and it is denoted by PSS. We consider the problem of inference associated with the nonnegative power, in the PSS class, with a member of SPD as a nuisance parameter. As the structural forms of the members of PSS are not known, one can’t directly use the sufficiency, invariance, or likelihood function. Hence by using certain properties of the SPD and the PSS classes, we identify maximal statistics whose distributions depend only on the power but not on the members of SPD. We then use the concept of minimal dimensionality for retaining the information about the parameter of interest. We use the minimax criterion, which leads to a statistic having Binomial distribution depending only on the parameter of interest. Hence inferences about the parameter of interest can be carried out using the standard methods for the binomial model. A simulation study indicates that the proposed estimator of the power parameter is asymptotically normal and is insensitive to the nuisance parameter. The proposed method is implemented for the analysis of a data set.

Suggested Citation

  • R. N. Rattihalli, 2023. "A Class of Multivariate Power Skew Symmetric Distributions: Properties and Inference for the Power-Parameter," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1356-1393, August.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00292-5
    DOI: 10.1007/s13171-022-00292-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-022-00292-5
    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/s13171-022-00292-5?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. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    2. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    3. Ian R. White, 2010. "simsum: Analyses of simulation studies including Monte Carlo error," Stata Journal, StataCorp LP, vol. 10(3), pages 369-385, September.
    4. Koehler, Elizabeth & Brown, Elizabeth & Haneuse, Sebastien J.-P. A., 2009. "On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses," The American Statistician, American Statistical Association, vol. 63(2), pages 155-162.
    5. Arnold, Steven F., 1985. "Sufficiency and invariance," Statistics & Probability Letters, Elsevier, vol. 3(5), pages 275-279, September.
    6. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, 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. Warrington Nicole M. & Tilling Kate & Howe Laura D. & Paternoster Lavinia & Pennell Craig E. & Wu Yan Yan & Briollais Laurent, 2014. "Robustness of the linear mixed effects model to error distribution assumptions and the consequences for genome-wide association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(5), pages 1-21, October.
    2. Ng'ombe, John, 2019. "Economics of the Greenseeder Hand Planter, Discrete Choice Modeling, and On-Farm Field Experimentation," Thesis Commons jckt7, Center for Open Science.
    3. Roger Tovar-Falón & Guillermo Martínez-Flórez & Heleno Bolfarine, 2022. "Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    4. Guillermo Martínez-Flórez & Diego I. Gallardo & Osvaldo Venegas & Heleno Bolfarine & Héctor W. Gómez, 2021. "Flexible Power-Normal Models with Applications," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    5. Guillermo Martínez-Flórez & Roger Tovar-Falón & Heleno Bolfarine, 2023. "The Log-Bimodal Asymmetric Generalized Gaussian Model with Application to Positive Data," Mathematics, MDPI, vol. 11(16), pages 1-14, August.
    6. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor Gómez, 2015. "Doubly censored power-normal regression models with inflation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 265-286, June.
    7. Guillermo Martínez-Flórez & Hector W. Gomez & Roger Tovar-Falón, 2021. "Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model," Mathematics, MDPI, vol. 9(16), pages 1-20, August.
    8. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor W. Gómez, 2017. "The Log-Linear Birnbaum-Saunders Power Model," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 913-933, September.
    9. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    10. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2021. "A model-free approach to multivariate option pricing," Review of Derivatives Research, Springer, vol. 24(2), pages 135-155, July.
    11. Jie Shi & Arno P. J. M. Siebes & Siamak Mehrkanoon, 2023. "TransCORALNet: A Two-Stream Transformer CORAL Networks for Supply Chain Credit Assessment Cold Start," Papers 2311.18749, arXiv.org.
    12. Tsai, Tsung-Han, 2016. "A Bayesian Approach to Dynamic Panel Models with Endogenous Rarely Changing Variables," Political Science Research and Methods, Cambridge University Press, vol. 4(3), pages 595-620, September.
    13. Vitoratou, Silia & Ntzoufras, Ioannis & Moustaki, Irini, 2016. "Explaining the behavior of joint and marginal Monte Carlo estimators in latent variable models with independence assumptions," LSE Research Online Documents on Economics 57685, London School of Economics and Political Science, LSE Library.
    14. Johannes Hönekopp & Audrey Helen Linden, 2022. "Heterogeneity estimates in a biased world," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-21, February.
    15. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
    16. Guillermo Martínez-Flórez & Carlos Barrera-Causil & Artur J. Lemonte, 2022. "Power Families of Bivariate Proportional Hazard Models," Mathematics, MDPI, vol. 10(23), pages 1-18, November.
    17. Sun-Joo Cho & Paul Boeck & Susan Embretson & Sophia Rabe-Hesketh, 2014. "Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 84-104, January.
    18. David A. Wagstaff & Ofer Harel, 2011. "A closer examination of three small-sample approximations to the multiple-imputation degrees of freedom," Stata Journal, StataCorp LP, vol. 11(3), pages 403-419, September.
    19. repec:jss:jstsof:43:i11 is not listed on IDEAS
    20. Michel Winter & Isabelle Mirbel & Pierre Crescenzo, 2014. "Modeling Uncertainty when Estimating IT Projects Costs," Working Papers hal-00966573, HAL.
    21. Squalli, Jay, 2017. "Renewable energy, coal as a baseload power source, and greenhouse gas emissions: Evidence from U.S. state-level data," Energy, Elsevier, vol. 127(C), pages 479-488.

    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:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00292-5. 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.