Term Selection for a Class of Separable Nonlinear Models In this paper, we consider the term selection problem for a class of separable nonlinear models. The strategy is a twostep process in which the nonlinear parameters of the model are first optimized by a variable projection method, and then the least absolute shrinkage and selection operator are adopted to obtain a sparse solution by picking out the critical terms automatically. This process may be repeated several times. The proposed algorithm is tested on parameter estimation problems for an exponential model and a neural networkbased model. The numerical results show that the proposed algorithm can pick out the appropriate terms from the overparameterized model and the obtained parsimonious model performs better than other methods.

Selection Consistency of LassoBased Procedures for Misspecified HighDimensional Binary Model and Random Regressors We consider selection of random predictors for a highdimensional regression problem with a binary response for a general loss function. An important special case is when the binary model is semiparametric and the response function is misspecified under a parametric model fit. When the true response coincides with a postulated parametric response for a certain value of parameter, we obtain a common framework for parametric inference. Both cases of correct specification and misspecification are covered in this contribution. Variable selection for such a scenario aims at recovering the support of the minimizer of the associated risk with large probability. We propose a twostep selection ScreeningSelection (SS) procedure which consists of screening and ordering predictors by Lasso method and then selecting the subset of predictors which minimizes the Generalized Information Criterion for the corresponding nested family of models. We prove consistency of the proposed selection method under conditions that allow for a much larger number of predictors than the number of observations. For the semiparametric case when distribution of random predictors satisfies linear regressions condition, the true and the estimated parameters are collinear and their common support can be consistently identified. This partly explains robustness of selection procedures to the response function misspecification.