Variable Selection For Additive Mixed-effects Model

On the condition that the number of nonzero functions is bounded or can tend to infinitywith the sample size, we study the variable selection for high-dimensional nonparametricadditive model. We use B spline to approximate the additive functions and transform thenonparametric additive model into ordinary linear model with approximate error. Then we proveout the consistency and sparsity properties of regression coefficients.We also construct a new model called additive mixed-effects model. Keep fixed effects thesame and replace random effects with additive functions, then we can get this new model. Theunknown varaibles are additive functions and covariance matrix. We use B spline to approximatethe additive functions and transform the additive mixed-effects model into mixed effect modelwith approximate error. The traditional variable selection methods can’t select fixed effects andrandom effects simultaneously. On the basic of adaptive Group LASSO method, we apply amodified Cholesky decomposition to covariance matrix. Then we can transform the selection ofrandom effects into the selection of diagonal elements of covariance matrix. The transformationmakes the simultaneous selection possible. Then we prove out the consistency and sparsityproperties of regression coefficients as well. The results show that we can identify the truenonparametric additive model and additive mixed-effects model with the probability tend to1...