Inference for Density Families Using Functional Principal Component Analysis

By Alois Kneip, Klaus J. Utikal. 2001

216 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2d4bf49b3e15fb0209db2e6668eb8cc98b304018

How researchers see this paper

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

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Wasserstein autoregressive models for density time series (2020, methodology): “An early approach to the analysis of distributional data by Kneip and Utikal (2001) used cross-sectional averaging and functional principal component analysis (FPCA) applied directly to yearly income densities.”
Properties of design-based functional principal components analysis (2008, methodology): “2009) as well as bootstrap properties (Kneip and Utikal, 2001) or sparse data (James et al.”
Peter Hall, functional data analysis and random objects (2016, background): “…situations where functional data lie in a subset or submanifold of a vector space that itself is not a vector space: Two prominent examples are random samples of density functions (Kneip and Utikal, 2001) and functional data with time warping components (Gasser, Sroka and Jennen-Steinmetz, 1986).”
Prediction by Supervised Principal Components (2006, methodology): “This follows from a refinement of the argument given in the proof of lemma A.1 of Kneip and Utikal (2001).”
Normal approximation and concentration of spectral projectors of sample covariance (2015, background): “The proofs of some of these facts that seem not to be readily available in the literature were given in [13] (see also Koltchinskii [15] and Kneip and Utikal [12] for some bounds in the same direction).”
Forecasting of density functions with an application to cross-sectional and intraday returns (2019, methodology): “Kneip and Utikal (2001) use kernel density estimation to obtain annual income densities, and study the temporal evolution of income density functions in the United Kingdom from 1968 to 1988.”
On properties of functional principal components analysis (2006, methodology): “…functional PCA in different metrics (e.g. Ocana et al. (1999)) and applications of PCA to fields as diverse as longitudinal data analysis (e.g. Yao et al. (2005)), time series analysis for functional data (e.g. Aguilera et al. (1999a, b)) and exploratory methods (e.g. Kneip and Utikal (2001)).”
COVARIATE ADJUSTED FUNCTIONAL PRINCIPAL COMPONENTS ANALYSIS FOR LONGITUDINAL DATA (2010, methodology): “Kneip and Utikal (2001) used methods of FDA to assess the variability of densities for data sets from different populations.”
Principal component analysis for functional data on Riemannian manifolds and spheres (2017, background): “Growth curve data (Ramsay and Silverman 2005) are examples of functions in a linear space, while densities (Kneip and Utikal 2001) and longitudinal shape profiles (Kent et al. 2001) lie on nonlinear manifolds.”
ASYMPTOTICS OF SAMPLE EIGENSTRUCTURE FOR A LARGE DIMENSIONAL SPIKED COVARIANCE MODEL (2007, methodology): “The approach taken here follows the perturbation analysis approach in Kneip and Utikal (2001), (see also Kato (1980, Chap.”
Functional Data Analysis (2016, background): “…with relative area-under-the curve warping, where the latter has been shown to be particularly well suited for samples of random density functions (Kneip & Utikal 2001; Zhang & M¨uller 2011) Recent approaches include registration by minimizing a Fisher-Rao metric (Tucker, Wu & Srivastava…”
Functional Data Analysis for Sparse Longitudinal Data (2005, background): “Various theoretical properties have been studied by Silverman (1996), Boente and Fraiman (2000), and Kneip and Utikal (2001).”
Factor models and variable selection in high-dimensional regression analysis (2011, unknown): “In order to verify (3.6) first note that Lemma A.1 of Kneip and Utikal (2001) implies that for symmetric matrices A and B ‖ψr(A+B)−ψr(A)‖2 ≤ ‖B‖ minj 6=r |λj(A)− λr(A)| (A.6) + 6‖B‖2 minj 6=r |λj(A)− λr(A)|2 , where ψ1(A), ψ2(A), . . . are the eigenvectors corresponding to the eigenvalues λ1(A)>…”
Nonparametric independent component analysis (2004, background): “It follows from Lemma A of Kneip and Utikal (2001), so we omit the proof.”
Functional Modelling and Classification of Longitudinal Data * (2005, background): “Examples of objects with special properties that are of interest are samples of density functions ( Kneip & Utikal, 2001 ) and hazard functions (Mu¨ ller et al., 1997).”
The Dynamics of Implied Volatilities: A Common Principal Components Approach (2003, background): “Even when smoothing and component estimation can be accomplished in one single step, this question seems to be mathematically unsolved ( Kneip and Utikal, 2001 ).”
Additive Functional Regression for Densities as Responses (2020, background): “…of densities as data objects have been proposed over the last decade (Egozcue, Diaz-Barrero, and Pawlowsky-Glahn 2006; Delicado 2007, 2011; Zhang and Müller 2011; Panaretos and Zemel 2016; Petersen and Müller 2016; Bigot et al. 2017), extending the pioneering work of Kneip and Utikal (2001).”