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Assessing the Distributional Assumptions in One-Way Regression Model

Kasturiratna, Dhanuja
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1148479945

Abstract Details

2006, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics/Probability and Statistics.
Characterization of the normal distribution related to k samples based on regression is given. This characterization has been transformed to a characterization based on Student's law. With the help of these characterization results, the composite hypothesis of testing the distributional assumptions in one-way regression model can be replaced by an equivalent simple hypothesis. This simple hypothesis can then be tested using any of the EDF goodness-of-fit tests. The powers of these tests are studied using Monte Carlo methods. Multivariate normal distribution, with covariance matrix of the form σ2Σ0, is characterized based on UMVU estimator of the density function. Using this result with the transformation proposed by Rincon-Gallardo, Quesenberry and O'Reilly (1979), the composite hypothesis of testing k-variate normality with covariance matrix σ2Σ0 has been transformed to an equivalent simple hypothesis. It is shown that the transformation proposed here can also be used in changing the above composite hypothesis to an equivalent simple hypothesis. These transformations are compared using Monte Carlo methods. Approximate EDF goodness of fit tests for testing the distributional assumptions in one-way regression model are studied using the Monte Carlo simulations.
Arjun Gupta (Advisor)
84 p.
Statistics
Conditional density function; UMVUE of the density function; Characteristic function; Differential equation; Moment; EDF; Power

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Citations

  • Kasturiratna, D. (2006). Assessing the Distributional Assumptions in One-Way Regression Model [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1148479945

    APA Style (7th edition)

  • Kasturiratna, Dhanuja. Assessing the Distributional Assumptions in One-Way Regression Model. 2006. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1148479945.

    MLA Style (8th edition)

  • Kasturiratna, Dhanuja. "Assessing the Distributional Assumptions in One-Way Regression Model." Doctoral dissertation, Bowling Green State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1148479945

    Chicago Manual of Style (17th edition)

bgsu1148479945
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© 2006, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.