No. 1083

Title:

Estimation of prediction error by using K-fold cross-validation

Author(s):

Fushiki, Tadayoshi (The Institute of Statistical Mathematics)

Key words:

Asymptotic theory, Bias correction, K-fold cross-validation.

Abstract:

    The estimation of prediction error is important when our aim is prediction. The training error is an easy estimate of prediction error, but it provides smaller prediction error on average. On the other hand, $K$-fold cross-validation provides larger prediction error on average. The over-estimate may be negligible in leave-one-out cross-validation, but it sometimes cannot be neglected in 5-fold and 10-fold cross-validation, which is favored from the computational viewpoint. Since the training error is an under-estimate and $K$-fold cross-validation is an over-estimate, there will be an appropriate estimate in a family which joins the two estimates. In this paper, we investigate two families which join the training error and $K$-fold cross-validation.