Consistency of cross-validation when the data are curves Academic Article uri icon

abstract

  • Suppose one observes a random sample of n continuous time Gaussian processes on the interval [0, 1]; in other words, each observation is a curve. Of interest is estimating the common mean function of the processes by a kernel smoother. The bandwidth of the kernel estimator is chosen by a version of cross-validation in which deleting an observation means deleting one of the n curves. It is shown that using this form of cross-validation leads to an asymptotically optimal choice of bandwidth. This result is contrasted with the inconsistency of cross-validation in a seemingly more tractable problem. © 1993.

author list (cited authors)

  • Hart, J. D., & Wehrly, T. E.

citation count

  • 25

publication date

  • April 1993