Functional Data Analysis for Sparse Longitudinal Data

By Fang Yao, H. Muller, Jane-ling Wang. 2005

1,693 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d181e0e761866792fba5607329f2ba69478a7972

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Citations in the corpus

Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes (2019, methodology): “For other observational designs, smoothing can be applied to the pooled data to estimate these quantities [26, 25].”
Partially Linear Functional Additive Models for Multivariate Functional Data (2018, methodology): “The most popular and best understood dimension reduction tool for functional data is the functional principal component analysis (FPCA) (Yao, Müller, and Wang 2005; Hall, Müller, and Wang 2006; Li and Hsing 2010b).”
A Geometric Approach to Maximum Likelihood Estimation of the Functional Principal Components From Sparse Longitudinal Data (2007, methodology): “To implement this, we employ a Newton-Raphson algorithm based on the work by Edelman, Arias and Smith (1998) for optimization on a Stiefel manifold, that utilizes its intrinsic Riemannian geometric structure.”
Diagnostic Checks for Multilevel Models (2008, background): “[62] present a model for irregular data with functions retrieved from a smooth estimate of the (continuous) covariance surface.”
Modelling function‐valued stochastic processes, with applications to fertility dynamics (2017, methodology): “Alternatively, one can recover the mean function μ by smoothing the pooled data (Yao et al., 2005), for example with a local linear smoother, obtaining a smoothing estimator μ̂.s, t/= â0, where .â0, â1, â2/=argmin 1 n n∑ i=1 Mi∑ m=1 Lim∑ l=1 [{Xi.tim, siml/−a0 −a1.siml − s/−a2.tim −…”
FUNCTIONAL RESPONSE MODELS (2004, methodology): “These can be overcome by employing alternative shrinkage estimators for functional principal component scores (Yao et al. (2003)).”
Smoothing splines estimators for functional linear regression (2009, background): “Our setup is inspired by other works dealing with noisy observations of functional data (e.g., Cardot [3] or Chiou, Müller and Wang [9]): At each point tj the corresponding functional value Xi(tj) is corrupted by some random error δij so that actual observations Wi(tj) are given by Wi(tj) = Xi(tj) ”
Asymptotic normality of the principal components of functional time series (2013, methodology): “[32,14], the FPCs vk are usually estimated by the empirical FPCs v̂k defined as the eigenfunctions of the empirical covariance operator  C(x) = N−1 N ”
Penalized spline models for functional principal component analysis (2006, methodology): “This lemma is particularly derived for the case of deterministic design points tij , whereas the random design was discussed in Yao et al. (2005).”
Estimation of the mean of functional time series and a two‐sample problem (2011, positive): “This issue has been extensively studied in one-sample problems, and several approaches have been put forward, including cross-validation and penalty criteria; see for example Müller and Stadtmüller (2005) and Yao et al. (2005).”
Conditional quantile analysis when covariates are functions, with application to growth data (2012, methodology): “More details can be found in Yao et al. (2005); these procedures are available in the PACE package, which is written in MATLAB and is available at http://anson.ucdavis.edu/∼mueller/data/pace.html.”
Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics (2009, methodology): “Then the number of repeated measurements Ni is assumed to be an iid bounded random variable (independent of other random variables).”
Optimal estimation of the mean function based on discretely sampled functional data: Phase transition (2011, background): “Instead, each curve is discretely observed at a different set of points [see, e.g., James and Hastie (2001), Rice and Wu (2001), Diggle et al. (2002), Yao, Müller and Wang (2005)].”
Modelling sparse generalized longitudinal observations with latent Gaussian processes (2008, background): “More details about this phenomenon can be found in Yao et al. (2005).”