  Image classification is considered, and a hierarchical max-pooling model with
additional local pooling is introduced. Here the additional local pooling
enables the hierachical model to combine parts of the image which have a
variable relative distance towards each other. Various convolutional neural
network image classifiers are introduced and compared in view of their rate of
convergence. The finite sample size performance of the estimates is analyzed by
applying them to simulated and real data.
