We simplify simplicial depth for regression and autoregressive growth processes in twodirections. At first we show that often simplicial depth reduces to counting the subsetswith alternating signs of the residuals. The second simplification is given by not regardingall subsets of residuals. By consideration of only special subsets of residuals,the asymptotic distributions of the simplified simplicial depth notions are normal distributionsso that tests and confidence intervals can be derived easily. We propose twosimplifications for the general case and a third simplification for the special case wheretwo parameters are unknown. Additionally, we derive conditions for the consistency ofthe tests. We show that the simplified depth notions can be used for polynomial regression,for several nonlinear regression models, and for several autoregressive growthprocesses. We compare the efficiency and robustness of the different simplified versionsby a simulation study concerning the Michaelis-Menten model and a nonlinearautoregressive process of order one.
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