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Author(s) -
Ramsay J. O.,
Li Xiaochun
Publication year - 1998
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00129
Subject(s) - functional data analysis , monotone polygon , nonparametric statistics , mathematics , range (aeronautics) , function (biology) , computer science , principal component analysis , transformation (genetics) , extension (predicate logic) , image warping , algorithm , statistics , artificial intelligence , geometry , biochemistry , materials science , chemistry , evolutionary biology , gene , composite material , biology , programming language
Functional data analysis involves the extension of familiar statistical procedures such as principal components analysis, linear modelling, and canonical correlation analysis to data where the raw observation x i is a function. An essential preliminary to a functional data analysis is often the registration or alignment of salient curve features by suitable monotone transformations h i of the argument t , so that the actual analyses are carried out on the values x i { h i ( t )}. This is referred to as dynamic time warping in the engineering literature. In effect, this conceptualizes variation among functions as being composed of two aspects: horizontal and vertical, or domain and range. A nonparametric function estimation technique is described for identifying the smooth monotone transformations h i , and is illustrated by data analyses. A second‐order linear stochastic differential equation is proposed to model these components of variation.