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Abstract: Bent-cable regression extends the popular piecewise linear
(broken-stick) model, allowing for a smooth change region of any non-negative
width. Existing bent-cable methodology assumes independent and identically
distributed errors. In this talk, we investigate data that exhibit a
bent-cable mean structure with noise generated by a low order autoregressive
model. A somewhat unorthodox sense of repeated experimentation is considered
when developing joint asymptotics of regression and
time series parameter estimators, based on conditional maximum likelihood.
Such estimators are shown to exhibit standard asymptotic properties
(consistency, asymptotic normality), despite non-differentiabilty
of the conditional score function. Physiological and atmospheric datasets are
presented to illustrate the methodology. Simulations demonstrate the above
asymptotic properties.
This is joint work with Prof. Richard
Lockhart of Simon
Fraser University.
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