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Prequential and cross-validated regression estimation
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DOI：10.1023/A:1007577530334.png)
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摘要
En 中文
Prequential model selection and delete-one cross-validation are data-driven methodologies for choosing between rival models on the basis of their predictive abilities. For a given set of observations, the predictive ability of a model is measured by the model's accumulated prediction error and by the model's average-out-of-sample prediction error, respectively, for prequential model selection and for cross-validation. In this paper, given i.i.d. observations, we propose nonparametric regression estimators-based on neural networks-that select the number of hidden units (or neurons) using either prequential model selection or delete-one cross-validation. As our main contributions: (i) we establish rates of convergence for the integrated mean-squared errors in estimating the regression function using off-line or batch versions of the proposed estimators and (ii) we establish rates of convergence for the time-averaged expected prediction errors in using on-line versions of the proposed estimators. We also present computer simulations (i) empirically validating the proposed estimators and (ii) empirically comparing the proposed estimators with certain novel prequential and cross-validated mixture regression estimators.
Keyword:
regression estimation
prequential model selection
cross-validation
neural networks
rates of convergence
mixture regression
integrated mean-squared error
time-averaged expected prediction error
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