seminars:stat:220407 [Department of Mathematics and Statistics, Binghamton University]

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<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>

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^  **DATE:**|Thursday, April 7, 2022 |
^  **TIME:**|1:15pm -- 2:15pm |
^  **LOCATION:**|Zoom meeting |
^  **SPEAKER:**|Yangsheng Wang, Binghamton University |
^  **TITLE:**|Recovering the Underlying Trajectory from Sparse and Irregular Longitudinal Data  |
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<WRAP centeralign>**Abstract**</WRAP>
In this article, we consider the problem of recovering the underlying
trajectory when the longitudinal data are sparsely and irregularly observed
and noise-contaminated. Such data are popularly analyzed with functional
principal component analysis via the principal analysis by conditional
estimation (PACE) method. The PACE method may sometimes be numerically
unstable because it involves the inverse of the covariance matrix. We
propose a sparse orthonormal approximation (SOAP) method as an alternative.
It estimates the optimal empirical basis functions in the best
approximation framework rather than eigen-decomposing the covariance
function. The SOAP method avoids estimating the mean and covariance
function, which is challenging when the assembled time points with
observations for all subjects are not sufficiently dense. The method also
avoids the inverse of the covariance matrix, hence the computation is more
stable. It does not require the functional principal component scores to
follow the Gaussian distribution. We show that the SOAP estimate for the
optimal empirical basis function is asymptotically consistent. The
finite-sample performance of the SOAP method is investigated in simulation
studies in comparison with the PACE method. Our method is demonstrated by
recovering the CD4 percentage curves from sparse and irregular data in a
multi-centre AIDS cohort study.
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