Nonparametric time dependent principal components analysis.

Abstract

In the biological sciences and elsewhere it is common to ignore the time depende nt component of the data (e.g. aged animals or year) when performing a principal component analysis (PCA). One way of incorporating this dimension or any other dependent variable is to perform PCA for the data at each time point or value of the dependent variable. The disadvantage of this approach is that there may not be enough data at each time point or dependent variable point. We overcome this by using a smoothed covariance or correlation matrix and by the choice of bandw idth we control the amount of neighbouring data contributing to the calculation. Permutations are used to construct reference bands to test whether there is a t ime effect. The techniques are illustrated on aircraft development data.