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Variable selection in sparse regression models is an important task asapplications ranging from biomedical research to econometrics have shown.Especially for higher dimensional regression problems, for which the linkfunction between response and covariates cannot be directly detected, theselection of informative variables is challenging. Under these circumstances,the Random Forest method is a helpful tool to predict new outcomes whiledelivering measures for variable selection. One common approach is the usage ofthe permutation importance. Due to its intuitive idea and flexible usage, it isimportant to explore circumstances, for which the permutation importance basedon Random Forest correctly indicates informative covariates. Regarding thelatter, we deliver theoretical guarantees for the validity of the permutationimportance measure under specific assumptions and prove its (asymptotic)unbiasedness. An extensive simulation study verifies our findings.

Asymptotic Unbiasedness of the Permutation Importance Measure in Random Forest Models