Optimal probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution nonparametrically over a given broad model class and proving asymptotic efficiency in that setting. The ideas are demonstrated within the context of...

Autoregressive models are commonly employed to analyze empirical time series. In practice, however, any autoregressive model will only be an approximation to reality and in order to achieve a reasonable approximation and allow for full generality the order of the autoregression, h say, must be...

We consider approximating a multivariate regression function by an affine combination of one-dimensional conditional component regression functions. The weight parameters involved in the approximation are estimated by least squares on the first-stage nonparametric kernel estimates. We establish...