This paper proposes an adaptive density estimation procedure that hinges on securing moment-based approximants of certain splines passing through particular points are obtained from appropriately adjusted and truncated empirical distribution function. More specifically, a four-parameter beta estimate is initially fitted to the data in order determine endpoints which combined points. Interpolant...

We study the power of deep neural networks (DNNs) with sigmoid activation function. Recently, it was shown that DNNs approximate any d-dimensional, smooth function on a compact set rate order W?p?d, where W is number nonzero weights in network and p smoothness Unfortunately, these rates only hold for special class sparsely connected DNNs. ask ourselves if we can show same approximation simpler ...