Nonparametric matrix regression function estimation over symmetric positive definite matrices
| Autor: | Peter T. Kim, Hongtu Zhu, Changyi Park, Kwang-Rae Kim, Ja-Yong Koo, Kwan-Young Bak |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Wishart distribution 05 social sciences Nonparametric statistics Estimator Positive-definite matrix 01 natural sciences 010104 statistics & probability Matrix (mathematics) Rate of convergence 0502 economics and business Applied mathematics 0101 mathematics Smoothing 050205 econometrics Mathematics Cholesky decomposition |
| Zdroj: | Journal of the Korean Statistical Society. 50:795-817 |
| ISSN: | 2005-2863 1226-3192 |
| Popis: | Symmetric positive definite matrix data commonly appear in computer vision and medical imaging, such as diffusion tensor imaging. The aim of this paper is to develop a nonparametric estimation method for a symmetric positive definite matrix regression function given covariates. By obtaining a suitable parametrization based on the Cholesky decomposition, we make it possible to apply univariate smoothing methods to the matrix regression problem. The parametrization also guarantees that the proposed estimator is symmetric positive definite over the entire domain. We adopt the Wishart log-likelihood and a smoothing technique using the basis methodology to define our estimator. The rate of convergence of the proposed estimator is obtained under some regularity conditions. Simulations are performed to investigate the finite sample properties of our proposed method using natural splines. Moreover, we present the results of an analysis of real diffusion tensor imaging data where the estimated fractional anisotropy is provided using $$3\times 3$$ symmetric positive definite matrices measured at consecutive positions along a fiber tract in the brain of subjects. |
| Databáze: | OpenAIRE |
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