COVARIATE ADJUSTED FUNCTIONAL PRINCIPAL COMPONENTS ANALYSIS FOR LONGITUDINAL DATA

By Ci-Ren Jiang, Jane-ling Wang. 2010

75 citations recorded by the source corpus.

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal of this paper to develop two methods that do. In the first approach, both the mean and covariance functions depend on the covariate $Z$ and time scale $t$ while in the second approach only the mean function depends on the covariate $Z$. Both new approaches accommodate additional measurement errors and functional data sampled at regular time grids as well as sparse longitudinal data sampled at irregular time grids. The first approach to fully adjust both the mean and covariance functions adapts more to the data but is computationally more intensive than the approach to adjust the covariate effects on the mean function only. We develop general asymptotic theory for both approaches and compare their performance numerically through simulation studies and a data set.

Subfields: Analytical Chemistry, Cognitive Neuroscience, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d63ee9f72cfd067383959428d32b8824da386ec9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

1. H. Muller
2. Jeng-Min Chiou
3. Jane-ling Wang
4. Jing Lei
5. Jan Peters
6. Stefan Bauer
7. Niklas Pfister
8. Han Lin Shang

In Cognitive Neuroscience

1. Jane-ling Wang
2. H. Muller

In Statistics and Probability

1. Jeng-Min Chiou
2. H. Muller
3. Jane-ling Wang
4. Han Lin Shang
5. Fang Yao
6. Sonja Greven
7. Peter Hall
8. H. ller

Citations in the corpus

• Functional single index models for longitudinal data (2011, unknown): “This lemma can be shown by following similar procedures as used to prove Lemma C.1 in Jiang and Wang (2010).”
• Functional Data Analysis (2016, background): “…& Wang 2003; Cardot 2007; Chiou & M¨uller 2009) for vector covariates and dense functional data, and also for sparse functional data with vector or functional covariates (Jiang & Wang 2010, 2011) and also to the case of functions in reproducing kernel Hilbert spaces (Amini & Wainwright 2012).”