Abstract
Ornstein-Uhlenbeck SDEs, where explicit calculations may be made for the postintervention
distributions.
Chapter 9 concerns identiability of the mixing matrix in ICA. It is a well-known
result that identiability of the mixing matrix depends crucially on whether the
error distributions are Gaussian or not. We attempt to elucidate what happens in
the case where the error distributions are close to but not exactly Gaussian.
Finally, Chapter 10 discusses degrees of freedom in nonlinear regression. Our motivating
problem is that of L1-constrained and L1-penalized estimation in nonlinear
regression. Our objective is to obtain results leading to the calculation of the degrees
of freedom of an estimator in order to enable sparse model selection by optimal
choice of the penalization parameter. We prove two results related to the degrees of
freedom, one theoretical result for constrained estimation, and one more practically
applicable for L1-penalized estimation.
distributions.
Chapter 9 concerns identiability of the mixing matrix in ICA. It is a well-known
result that identiability of the mixing matrix depends crucially on whether the
error distributions are Gaussian or not. We attempt to elucidate what happens in
the case where the error distributions are close to but not exactly Gaussian.
Finally, Chapter 10 discusses degrees of freedom in nonlinear regression. Our motivating
problem is that of L1-constrained and L1-penalized estimation in nonlinear
regression. Our objective is to obtain results leading to the calculation of the degrees
of freedom of an estimator in order to enable sparse model selection by optimal
choice of the penalization parameter. We prove two results related to the degrees of
freedom, one theoretical result for constrained estimation, and one more practically
applicable for L1-penalized estimation.
| Original language | English |
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| Publisher | Department of Mathematical Sciences, Faculty of Science, University of Copenhagen |
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| Number of pages | 246 |
| ISBN (Print) | 978-87-7078-386-6 |
| Publication status | Published - 2013 |