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  • 1.
    Hao, Chengcheng
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Liang, Yuli
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Roy, Anuradha
    Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data2015In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 106, p. 113-120Article in journal (Refereed)
    Abstract [en]

    Centers and vertices principal component analyses are common methods to explain variations within multivariate interval data. We introduce multivariate equicorrelated structures to vertices’ covariance. Assuming the structure, we show equivalence between centers and vertices methods by proving their eigensystems proportional.

  • 2.
    Liang, Yuli
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Contributions to Estimation and Testing Block Covariance Structures in Multivariate Normal Models2015Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis concerns inference problems in balanced random effects models with a so-called block circular Toeplitz covariance structure. This class of covariance structures describes the dependency of some specific multivariate two-level data when both compound symmetry and circular symmetry appear simultaneously.

    We derive two covariance structures under two different invariance restrictions. The obtained covariance structures reflect both circularity and exchangeability present in the data. In particular, estimation in the balanced random effects with block circular covariance matrices is considered. The spectral properties of such patterned covariance matrices are provided. Maximum likelihood estimation is performed through the spectral decomposition of the patterned covariance matrices. Existence of the explicit maximum likelihood estimators is discussed and sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and the corresponding maximum likelihood estimators are presented.

    This thesis also deals with hypothesis testing of block covariance structures, especially block circular Toeplitz covariance matrices. We consider both so-called external tests and internal tests. In the external tests, various hypotheses about testing block covariance structures, as well as mean structures, are considered, and the internal tests are concerned with testing specific covariance parameters given the block circular Toeplitz structure. Likelihood ratio tests are constructed, and the null distributions of the corresponding test statistics are derived.

  • 3.
    Liang, Yuli
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    På väg att lära sig statistik2014In: Qvintense, ISSN 2000-1819, Vol. 3, p. 6-7Article in journal (Other (popular science, discussion, etc.))
  • 4.
    Liang, Yuli
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    von Rosen, Dietrich
    Tatjana, von Rosen
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    On estimation in multilevel models with block circular symmetric covariance structure2012In: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 16, no 1, p. 83-96Article in journal (Refereed)
    Abstract [en]

    In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

  • 5.
    Liang, Yuli
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    von Rosen, Dietrich
    von Rosen, Tatjana
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    On estimation in hierarchical models with block circular covariance structures2015In: Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, E-ISSN 1572-9052, Vol. 67, no 4, p. 773-791Article in journal (Refereed)
    Abstract [en]

    Hierarchical linear models with a block circular covariance structure are considered. Sufficient conditions for obtaining explicit and unique estimators for the variance–covariance components are derived. Different restricted models are discussed and maximum likelihood estimators are presented. The theory is illustrated through covariance matrices of small sizes and a real-life example.

  • 6.
    Liang, Yuli
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    von Rosen, Dietrich
    von Rosen, Tatjana
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    Testing in multivariate normal models with block circular covariance structures2015Report (Other academic)
    Abstract [en]

    In this article, the results concerning hypothesis testing in multivariate normal models with block circular covariance structures are obtained. Hypotheses about a general block structure of the covariance matrix and specific covariance parameters have been of main interest. In addition, the tests about patterned mean vectors have been considered.The corresponding likelihood ratio statistics are derived and their null distributions are studied.

  • 7.
    Liang, Yuli
    et al.
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    von Rosen, Tatjana
    Stockholm University, Faculty of Social Sciences, Department of Statistics.
    von Rosen, Dietrich
    Block Circular Symmetry in Multilevel Models2011Report (Other academic)
    Abstract [en]

    Models that describe symmetries present in the error structure of observations have been widely used in dierent applications, with early examples from psychometric and medical research. The aim of this article is to study a multilevel model with a covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.

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