Regularized Nonlinear Regression with Dependent Errors and its Application to a Biomechanical ModelA biomechanical model often requires parameter estimation and selection in a
known but complicated nonlinear function. Motivated by observing that data from
a head-neck position tracking system, one of biomechanical models, show
multiplicative time dependent errors, we develop a modified penalized weighted
least squares estimator. The proposed method can be also applied to a model
with non-zero mean time dependent additive errors. Asymptotic properties of the
proposed estimator are investigated under mild conditions on a weight matrix
and the error process. A simulation study demonstrates that the proposed
estimation works well in both parameter estimation and selection with time
dependent error. The analysis and comparison with an existing method for
head-neck position tracking data show better performance of the proposed method
in terms of the variance accounted for (VAF).
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