Browsing by Subject "consistency"

Now showing 1 - 2 of 2
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    Large-sample estimation and inference in multivariate single-index models
    (Elsevier, 2019-05) Wu, Jingwei; Peng, Hanxiang; Tu, Wanzhu; Mathematical Sciences, School of Science
    By optimizing index functions against different outcomes, we propose a multivariate single-index model (SIM) for development of medical indices that simultaneously work with multiple outcomes. Fitting of a multivariate SIM is not fundamentally different from fitting a univariate SIM, as the former can be written as a sum of multiple univariate SIMs with appropriate indicator functions. What have not been carefully studied are the theoretical properties of the parameter estimators. Because of the lack of asymptotic results, no formal inference procedure has been made available for multivariate SIMs. In this paper, we examine the asymptotic properties of the multivariate SIM parameter estimators. We show that, under mild regularity conditions, estimators for the multivariate SIM parameters are indeed
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    Semiparametric partial common principal component analysis for covariance matrices
    (Wiley, 2021-12) Wang, Bingkai; Luo, Xi; Zhao, Yi; Caffo, Brian; Biostatistics, School of Public Health
    We consider the problem of jointly modeling multiple covariance matrices by partial common principal component analysis (PCPCA), which assumes a proportion of eigenvectors to be shared across covariance matrices and the rest to be individual-specific. This paper proposes consistent estimators of the shared eigenvectors in the PCPCA as the number of matrices or the number of samples to estimate each matrix goes to infinity. We prove such asymptotic results without making any assumptions on the ranks of eigenvalues that are associated with the shared eigenvectors. When the number of samples goes to infinity, our results do not require the data to be Gaussian distributed. Furthermore, this paper introduces a sequential testing procedure to identify the number of shared eigenvectors in the PCPCA. In simulation studies, our method shows higher accuracy in estimating the shared eigenvectors than competing methods. Applied to a motor-task functional magnetic resonance imaging data set, our estimator identifies meaningful brain networks that are consistent with current scientific understandings of motor networks during a motor paradigm.