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Nonparametric Covariance Estimation for Longitudinal Data

Blake, Tayler Ann, Blake
http://orcid.org/0000-0003-2275-9600
http://rave.ohiolink.edu/etdc/view?acc_num=osu15256491898913

Abstract Details

2018, Doctor of Philosophy, Ohio State University, Statistics.
Estimation of an unstructured covariance matrix is difficult because of the challenges posed by parameter space dimensionality and the positive definiteness constraint that estimates should satisfy. We propose a general framework for nonparametric covariance estimation for longitudinal data where the variables have a natural ordering. Modeling the Cholesky decomposition of the covariance matrix removes constraints from estimation, including those posed by positive definiteness. In addition, the Cholesky decomposition enjoys the added advantage over alternative matrix decompositions by supplying a meaningful statistical interpretation of the corresponding estimated parameters. We illustrate the equivalence of covariance estimation and the estimation of a varying coefficient autoregressive model. By defining the varying coefficient as a bivariate function, we naturally accommodate sparsely or irregularly sampled longitudinal data without the need for imputation. This framework extends the set of tools available for covariance estimation to any of those employed in the typical function estimation setting. Viewing stationarity as a form of simplicity or parsimony in covariance models, we specify the varying coefficient as a function so that we can conveniently penalize the components capturing the nonstationarity in the fitted function. Casting covariance estimation as bivariate smoothing problem, we demonstrate construction of a covariance estimator using the smoothing spline framework and a penalized B-spline expansion. A simulation study establishes the advantage of our estimator over alternative estimators proposed in this setting. We analyze a longitudinal dataset to illustrate application of the methodology and compare our estimates to those resulting from alternative models proposed for the covariance for longitudinal data.
Yoonkyung Lee, PhD (Advisor)
163 p.
Statistics
longitudinal data, Hilbert space, nonparametric function estimation, covariance estimation

Recommended Citations

Citations

  • Blake, Blake, T. A. (2018). Nonparametric Covariance Estimation for Longitudinal Data [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu15256491898913

    APA Style (7th edition)

  • Blake, Blake, Tayler. Nonparametric Covariance Estimation for Longitudinal Data. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu15256491898913.

    MLA Style (8th edition)

  • Blake, Blake, Tayler. "Nonparametric Covariance Estimation for Longitudinal Data." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu15256491898913

    Chicago Manual of Style (17th edition)

osu15256491898913
608
© 2018, some rights reserved.Creative Commons License Nonparametric Covariance Estimation for Longitudinal Data by Tayler Ann Blake Blake is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.