Incorporating Parametric Effects into Functional Principal Components Analysis
扩展函数型主成分分析，处理同时包含函数型和参数效应的混合数据，以加拿大35个气象站的温度数据为例，展示了用Procrustes拟合方法估计参数效应。
SUMMARY The ideas of functional principal component analysis are extended to deal with data that are hybrids of ‘functional’ and ‘parametric’ effects. The parametric effects may be more general than just the addition of a multiple of a given function. A detailed development is given in the case of shifts of the time axis for functions observed on a periodic interval, and some remarks are made for the extension to a far more general case. Given data, a Procrustes fitting method can be used to estimate the parametric effects. Several possible ways of treating the estimated parameter values are discussed. The methods are illustrated by reference to temperature data at 35 Canadian weather-stations.