  In a regression model, prediction is typically performed after model
selection. The large variability in the model selection makes the prediction
unstable. Thus, it is essential to reduce the variability in model selection
and improve prediction accuracy. To achieve this goal, a parametric bootstrap
smoothing can be applied. In this method, model selection is performed for each
resampling from a parametric distribution, and these models are then averaged
such that the distribution of the selected models is considered. Here, the
prediction accuracy is highly dependent on the choice of a distribution for
resampling. In particular, an experimental study shows that the choice of error
variance significantly changes the distribution of the selected model and thus
plays a key role in improving the prediction accuracy. We also observed that
the true error variance does not always provide optimal prediction accuracy.
Therefore, it would not always be appropriate to use unbiased estimators of the
true parameters or standard estimators of the parameters for the resampling
distribution. In this study, we propose employing cross validation to choose a
suitable resampling distribution rather than unbiased estimators of parameters.
Our proposed method was applied to electricity demand data. The results
indicate that the proposed method provides a better prediction accuracy than
the existing method.
