Degrees of Freedom in Functional Principal Components Analysis

Zixin Lin

Mathematical Problems in Engineering, 2021, vol. 2021, 1-11

Abstract:

This paper develops the analytical form of the degrees of freedom in functional principal components analysis. Under the framework of unbiased risk estimation, we derive an unbiased estimator with a clear analytical formula for the degrees of freedom in the one-way penalized functional principal components analysis paradigm. Specifically, a new analytical formula incorporating binary smoothing parameters is also derived based on the singular value decomposition and half-smoothed method regarding the two-way penalized functional principal components analysis framework. The performance of our procedures is demonstrated by simulation studies.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8992841

DOI: 10.1155/2021/8992841

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