[Gretl-users] Re: Estimation of a State Space model with constrained parameters
Am 30.09.2021 um 16:32 schrieb Paolo Chirico:
Hi,
I have to estimate a State Space model where a parameter must have
values in a range (between two limit values: L1 and L2)
I can't define the derivates (i.e. numeric MLE).
Do you have any suggestions?
Hi, the standard trick would be to map the parameter to an unrestricted
range for example with a CDF (or actually, its inverse). So for example,
you have the restriction L1 < beta < L2. You could replace beta by: L1 +
cdf(b) * (L2-L1). Since cdf(b) is always between 0 and 1, the whole
expression will be between L1 and L2 by construction, honoring your
restriction. But b is freely varying, so formally no constrained
estimation is needed. And the mapping is monotonous.
Of course if you need standard errors for beta, things get more
complicated, but at the boundaries L1 and L2 they're not well defined
anyway, I'd say.
The above is just an example, surely not the most efficient solution.
cheers
sven