Model Related Instabilities in High Dimensional Linear Models

The use of high dimensional linear models is common in large database settings. The linearity of such models is often assumed. In sparse settings with the number of subjects (n) less than the number of variables (p) standard algorithms include the lars-LASSO approach which often provides stable convergence. In some cases the underlying data may be more appropriately modeled with a nonlinear model. The use of a linear model in such cases creates model mis-specification and instability for lars-LASSO based approaches. This is studied by using simulations with various relative sample sizes, correlation structures and error distributions.