NONPARAMETRIC-ESTIMATION OF THE MODE OF A DISTRIBUTION OF RANDOM CURVES

Motivated by the need to develop meaningful empirical approximations t o a 'typical' data value, we introduce methods for density and mode es timation when data are in the form of random curves. Our approach is b ased on finite dimensional approximations via generalized Fourier expa nsions on an empirically chosen basis. The mode estimation problem is reduced to a problem of kernel-type multivariate estimation from vecto r data and is solved using a new recursive algorithm for finding the e mpirical mode. The algorithm may be used as an aid to the identificati on of clusters in a set of data curves. Bootstrap methods are employed to select the bandwidth.