Jaromír Antoch
Keywords: Linear regression, structural changes,
-procedures, permutation principle, Monte Carlo, change-point
problem.
We consider the regression model with a change after an unknown time
point , i.e.
where ,
and
are unknown parameters,
are
known design points and
are iid random errors
fulfilling regularity conditions specified below. Function
denotes the indicator of the set
.
Model () describes the situation where the first
observations follow the linear model with the parameter
and the remaining
observations follow the linear
regression model with the parameter
. The parameter
is usually called the change point.
In the lecture we focus on the testing problem:
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(2) |
Approximations to the critical values needed for this testing problem
can be obtained through the limit distribution of the respective test
statistics under , however, such approximations are usually not
satisfactory. Therefore, we proposed another possibility, namely, the
approximations based on the application of the permutational principle,
of course, suitably modified for the situation of regression models. We
will discuss this approach in the lecture and give some examples based
on real data illustrating its advantages and disadvantages.