Descriptions of Functional Data
This chapter and the next are the exploratory data analysis end of functional data analysis. Here we recast the concepts of mean, standard deviation, covariance and correlation into functional terms and provide R and Matlab functions for computing and viewing them.
Exploratory tools are often the most fruitful when applied to residual variation around some model, where we often see surprising effects once we have removed relatively predictable structures from the data. Summary descriptions of residual variation are also essential for estimating confidence regions.
Contrasts are often used in analysis of variance to explore prespecified patterns of variation.We introduce the more general concept of a functional probe as a means of looking for specific patterns or shapes of variation in functional data and of providing methods for estimating confidence limits for estimated probe values.
KeywordsFunctional Data Functional Data Analysis Functional Probe Large Cycle Roughness Penalty
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