Vol 27, No 2 (2018)

The problem of statistical parameter estimation is considered for binary GLM-based autoregression with the link function of general form and the base functions (regressors) nonlinear w.r.t. the lagged variables. A new consistent asymptotically normal frequencies-based estimator (FBE) is constructed and compared with the classical MLE. It is shown that the FBE has less restrictive sufficient conditions of uniqueness than the MLE (does not need log-concavity of the inverse link) and can be computed recursively under the model extension. The sparse version of the FBE is proposed and the optimal model-dependent weight matrices (parameterizing the FBE) are found for the FBE and for the sparse FBE. The proposed empirical choice of the subset of s-tuples for the sparse FBE is examined by numerical and analytical examples. Computer experiments for comparison of the FBE versus the MLE are performed on simulated and real (genetic) data.

When the classical nonparametric bootstrap is implemented by a Monte-Carlo procedure one resamples values from a sequence of, typically, independent and identically distributed ones. But what happens when a decision has to be taken based on such resampled values? One way to quantify the loss of information due to this resampling step is to consider the deficiency distance, in the sense of Le Cam, between a statistical experiment of n independent and identically distributed observations and the one consisting of m observations taken from the original n by resampling with replacement. By comparing with an experiment where only subsamplingwith a random subsampling size has been performed one can bound the deficiency in terms of the amount of information contained in additional observations. It follows for certain experiments that the deficiency distance is proportional to the expected fraction of observations missed when resampling.