Simplified simplicial depth for regression and autoregressive growth processes
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Date
2014-10-09
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Abstract
We simplify simplicial depth for regression and autoregressive growth processes in two
directions. At first we show that often simplicial depth reduces to counting the subsets
with alternating signs of the residuals. The second simplification is given by not regarding
all subsets of residuals. By consideration of only special subsets of residuals,
the asymptotic distributions of the simplified simplicial depth notions are normal distributions
so that tests and confidence intervals can be derived easily. We propose two
simplifications for the general case and a third simplification for the special case where
two parameters are unknown. Additionally, we derive conditions for the consistency of
the tests. We show that the simplified depth notions can be used for polynomial regression,
for several nonlinear regression models, and for several autoregressive growth
processes. We compare the efficiency and robustness of the different simplified versions
by a simulation study concerning the Michaelis-Menten model and a nonlinear
autoregressive process of order one.
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Keywords
alternating sign, consistency, asymptotic distribution, robustness, distribution-free test