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    A mixed model for complete three or higher-way layout with two random effects factors
    (Elsevier Inc, 2015) Guven, Bilgehan
    The classical F-test for testing the hypothesis of no fixed main effects in a mixed model is valid under normality, variance homogeneity and symmetry assumption. We consider a mixed model in which one fixed and two random main effects are crossed. A new test procedure for testing the hypothesis of no fixed main effects is developed under violations of normality, variance homogeneity and symmetry assumptions. The asymptotic distribution of the proposed test statistic is studied under the condition that the numbers of levels of two main random effects are large. The asymptotic distribution of the test statistic is the chi-square distribution. The theory presented in this article is applicable for complete four or higher-way layout with two random factors. (C) 2015 Elsevier Inc. All rights reserved.
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    APPROXIMATE TEST FOR TESTING A NULL VARIANCE RATIO IN THE UNBALANCED ONE-WAY RANDOM MODEL
    (Ankara Univ, Fac Sci, 2020) Demircioglu, Sevgi; Guven, Bilgehan
    The approximate test for testing the significance of the random effect is presented in the unbalanced one-way random model in which both random effects and errors are from nonnormal universes. The test is based on the asymptotic distribution of the F-ratio. Under the condition that the number of groups tends to infinity while the average of powers of the group sizes is bounded, the asymptotic distribution of the F statistic is obtained. Robustness of the proposed test is given.
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    Approximate tests in unbalanced two-way random models without interaction
    (Springer, 2012) Guven, Bilgehan
    In the presence of non-normality, we consider testing for the significance of the variance components in the unbalanced two-way random model without interaction. The approximate test is based on the F-statistic for this model. The asymptotic distribution of the F-statistic is derived as the number of treatments tends to infinity while the number of observations for a treatment in any block takes value from a finite set of positive integers. Robustness of the approximate test is given.
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    Testing for random effect in the Fuller-Battese model
    (Taylor & Francis Ltd, 2014) Guven, Bilgehan
    We consider the Fuller-Battese model where random effects are allowed to be from non-normal universes. The asymptotic distribution of the F-statistic in this model is derived as the number of groups tends to infinity (is large) and sample size from any group is either fixed or large. The result is used to establish an approximate test for the significance of the random effect variance component. Robustness of the established approximate test is given.
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    The spectral decomposition of a covariance matrix for the balanced mixed analysis of variance model
    (Elsevier Science Inc, 2012) Guven, Bilgehan
    We derive the spectral decomposition of a covariance matrix for the balanced mixed analysis of variance model. The derivation is based on determining the distinct eigenvalues of a covariance matrix and then obtaining a principal idempotent matrix for each distinct eigenvalue. Examples are given to illustrate the results. (C) 2011 Elsevier Inc. All rights reserved.