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.

Comparison of Variable Selection Methods for Forecasting from Short Time Series Forecasting from multivariate time series data is a difficult task, made more so in the situation where the number of series (p) is much larger than the length of each series (T), which makes dimension reduction desirable prior to obtaining a model. The LASSO has become a widelyused method to choose relevant covariates out of many candidates, and it has many variations and extensions, such as grouped LASSO, adaptive LASSO, weighted lag adaptive LASSO, and fused LASSO. Of these, only the weighted lag adaptive LASSO and the fused LASSO take into account natural ordering among series. To examine the ability of variations on the LASSO to choose relevant covariates for short time series we use simulations for series with fewer than 50 observations. We then apply the methods to a data set on significant changes in selfreported psychosocial symptoms in the 30 years after the Chornobyl nuclear catastrophe.