Optimally adjusted last cluster for prediction based on balancing the bias and variance by bootstrapping

Estimating a predictive model from a dataset is best initiated with an unbiased estimator. However, since the unbiased estimator is unknown in general, the problem of the bias-variance tradeoff is raised. Aside from searching for an unbiased estimator, the convenient approach to the problem of the bias-variance tradeoff may be to use the clustering method. Within a cluster whose size is smaller than the whole sample, we would expect the simple form of the estimator for prediction to avoid the overfitting problem. In this paper, we propose a new method to find the optimal cluster for prediction. Based on the previous literature, this cluster is considered to exist somewhere between the whole dataset and the typical cluster determined by partitioning data. To obtain a reliable cluster size, we use the bootstrap method in this paper. Additionally, through experiments with simulated and real-world data, we show that the prediction error can be reduced by applying this new method. We believe that our proposed method will be useful in many applications using a clustering algorithm for a stable prediction performance.