Functional data analysis (FDA) 发表评论(0) 编辑词条

Functional data analysis (FDA) addresses the analysis of information on curves or functions. As an example, FDA can be useful for analyzing growth curves of children that are constructed based on body height measurements made over some specific growing period. In this example, FDA would treat one growth curve as one functional data entity. Without any assumption on the parametric forms for growth curves, the discrete measurements for body heights can be transferred into a continuous curve by nonparametric smoothing. With FDA we study many important features of curves such as growth rates, which are derivatives of growth curves. In fact, it is the many uses of derivatives that are the central theme of FDA. Topics in FDA include:

1. Curve Registration: Align multiple curves with similar shapes by transformation in the time domain.

2. Functional Principal Component analysis: Finding major variations among multiple curves.

3. Functional Linear Models: Estimating relationships between functions.

4. Estimating Differential Equations from real data: including ordinary, partial, or stochastic differential equations.

5. Estimating Constrained Functions: The constraints can be positive functions, or strictly monotone functions, etc.