Consistency of cross-validation when the data are curves

Jeffrey D. Hart and Thomas E. Wehrly

Stochastic Processes and their Applications, 1993, vol. 45, issue 2, 351-361

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.

Keywords: kernel; estimator; Gaussian; processes; covariance; function; bandwidth; selection (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (11)

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