Book Chapter10.1007/978-3-540-32691-5_16
Functional Data Analysis
Michal Benko
- 01 Jan 2007
- pp 305-327
157
TL;DR: In this article, the authors introduce the functional data analysis (FDA), discuss the practical usage and implementation of the FDA methods, and propose a stochastic model for functional data and statistical analysis of functional data set can be taken often onetoone from the conventional multivariate analysis.
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Abstract: In many different fields of applied statistics the object of interest is depending on some continuous parameter, i.e. continuous time. Typical examples in biostatistics are growth curves or temperature measurements. Although for technical reasons, we are able to measure temperature just in discrete intervals — it is clear that temperature is a continuous process. Temperature during one year is a function with argument “time”. By collecting one-year-temperature functions for several years or for different weather stations we obtain bunch (sample) of functions — functional data set. The questions arising by the statistical analysis of functional data are basically identical to the standard statistical analysis of univariate or multivariate objects. From the theoretical point, design of a stochastic model for functional data and statistical analysis of the functional data set can be taken often one-to-one from the conventional multivariate analysis. In fact the first method how to deal with the functional data is to discretize them and perform a standard multivariate analysis on the resulting random vectors. The aim of this chapter is to introduce the functional data analysis (FDA), discuss the practical usage and implementation of the FDA methods.
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References
•Book
The Elements of Statistical Learning
Trevor Hastie,Robert Tibshirani,Jerome H. Friedman +2 more
- 01 Jan 2001
29.4K
Functional Data Analysis
James O. Ramsay,Bernard W. Silverman +1 more
- 01 Jan 2001
TL;DR: In this article, the authors introduce the concept of functional data analysis (FDA) to describe the smoothness of the process of generating functional data from a set of observed curves and images.
1.5K
Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
TL;DR: In this paper, the results of convergence by sampling in linear principal component analysis (LPCA) were derived for a random function in a separable Hilbert space, and the limiting distribution was given for the principal values and the principal factors.
538
Inference for Density Families Using Functional Principal Component Analysis
TL;DR: In this article, a detailed asymptotic theory is presented for the analysis of yearly cross-sectional samples of British households from 1968-1988, which provides new insights into the evolution and interplay of household income and age distributions.
247