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    Statistical Modeling using Conditionally Specified Joint Distributions with Applications

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    Wijekoon_umbc_0434D_12471.pdf (2.467Mb)
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    http://hdl.handle.net/11603/26034
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    • UMBC Graduate School
    • UMBC Mathematics and Statistics Department
    • UMBC Student Collection
    • UMBC Theses and Dissertations
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    Author/Creator
    Wijekoon, Nadeesri
    Date
    2021-01-01
    Type of Work
    application:pdf
    Text
    dissertation
    Department
    Mathematics and Statistics
    Program
    Statistics
    Rights
    This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu
    Distribution Rights granted to UMBC by the author.
    Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan thorugh a local library, pending author/copyright holder's permission.
    Subjects
    Compatibility
    Composite Likelihood
    Conditional Specification
    Conditionally Specified Models
    Joint Asymptotic Relative Efficiency
    Abstract
    Often in practice, conditional distributions are easier to model and interpret while the joint distribution itself is either intractable or not available in closed form. When the observed response consists of both continuous and discrete components, specifying conditionals is more convenient. There are many real-world applications where the conditional specification approach is intuitively appealing, and knowing the conditional distributions makes it easier to understand and visualize the joint distribution. Furthermore, the researcher can obtain a better insight by investigating and interpreting the conditional distributions. In this thesis, we propose a joint distribution that can be specified using its respective conditionals and which can handle both continuous data and discrete data together. In literature, such models are referred to as conditionally specified models. We explored the theoretical aspects of conditionally specified models, where conditionals are from the exponential family of distributions, including parameter estimation, data generation, and uniqueness of the joint distributions. The Maximum Likelihood (ML) method, which is the preferred estimation method of parametric models, turns out to be difficult to implement for estimating the parameters of conditionally specified joint distributions because it contains an awkward normalizing constant. Thus, Composite Likelihood (CL) was used as an alternative method of estimation. We used numerical methods to obtain the estimates of parameters since closed-form expressions for estimates using the proposed density are not feasible. Simulation studies were conducted for different sample sizes to investigate the properties of ML estimates and CL. It showed that the ML method has less bias (and nearly zero in some cases) than the CL method, however, the CL method involves relatively less computational burden. In both methods, the variances of the estimates decrease as the sample size increases. Further, joint asymptotic relative efficiency (JARE) between the ML method and CL method were calculated for different sample sizes using the Godambe Information matrix. In addition, we conducted a performance analysis utilizing the two methods. The results showed that for a larger sample size, the computational advantage of the CL method surpasses that of the ML method quickly. Thus, choosing the CL method over the ML method is a trade-off between efficiency and computational cost. The proposed normal-logistic joint density was applied to the stock prices (continuous data) and expert recommendations (categorical data) for buying/selling specific stocks. Parameters of the model were estimated using both ML and CL methods.


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3021


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.