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A Class of Multivariate Skew Distributions: Properties and Inferential Issues

Akdemir, Deniz
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643

Abstract Details

2009, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics/Probability and Statistics.
Flexible parametric distribution models that can represent both skewed and symmetric distributions, namely skew symmetric distributions, can be constructed by skewing symmetric kernel densities by using weighting distributions. In this dissertation, we study a multivariate skew family that have either centrally symmetric or spherically symmetric kernel. Specifically, we define multivariate skew symmetric forms of uniform, normal, Laplace, and Logistic distributions by using the cdf's of the same distributions as weighting distributions. Matrix variate extensions of these distributions are also introduced herein. To bypass the unbounded likelihood problem related to the inference about this model, we propose an estimation procedure based on the maximum product of spacings method. This idea also leads to bounded model selection criteria that can be considered as alternatives to Akaike's and other likelihood based criteria when the unbounded likelihood may be a problem. Applications of skew symmetric distributions to data are also considered.
Arjun K. Gupta, PhD (Advisor)
James M. McFillen, PhD (Committee Chair)
John T. Chen, PhD (Committee Member)
Hanfeng Chen, PhD (Committee Member)
116 p.
Statistics
Multivariate Skew-Symmetric Distribution; Matrix Variate Skew-Symmetric Distribution; Inference, Maximum Product of Spacings; Unbounded Likelihood, Model Selection Criterion

Recommended Citations

Citations

  • Akdemir, D. (2009). A Class of Multivariate Skew Distributions: Properties and Inferential Issues [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643

    APA Style (7th edition)

  • Akdemir, Deniz. A Class of Multivariate Skew Distributions: Properties and Inferential Issues. 2009. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643.

    MLA Style (8th edition)

  • Akdemir, Deniz. "A Class of Multivariate Skew Distributions: Properties and Inferential Issues." Doctoral dissertation, Bowling Green State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1237574643

    Chicago Manual of Style (17th edition)

bgsu1237574643
2,101
© 2009, some rights reserved.Creative Commons License A Class of Multivariate Skew Distributions: Properties and Inferential Issues by Deniz Akdemir is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Bowling Green State University and OhioLINK.