New model search for nonlinear recursive models, regressions and autoregressions - Anna-Lena Kißlinger, Wolfgang Stummer
Author(s): Anna-Lena Kißlinger, Wolfgang Stummer
DOI URL: http://dx.doi.org/10.1007/978-3-319-25040-3_74
Creative Commons Attribution-ShareAlike 4.0 International
Scaled Bregman distances SBD have turned out to be useful tools for simultaneous estimation and goodness-of-fit-testing in parametric models of random data (streams, clouds). We show how SBD can additionally be used for model preselection (structure detection), i.e. for finding appropriate candidates of model (sub)classes in order to support a desired decision under uncertainty. For this, we exemplarily concentrate on the context of nonlinear recursive models with additional exogenous inputs; as special cases we include nonlinear regressions, linear autoregressive models (e.g. AR, ARIMA, SARIMA time series), and nonlinear autoregressive models with exogenous inputs (NARX). In particular, we outline a corresponding information-geometric 3D computer-graphical selection procedure. Some sample-size asymptotics is given as well.