TY - BOOK

T1 - On Martingales, Causality, Identifiability and Model Selection

AU - Sokol, Alexander

PY - 2013

Y1 - 2013

N2 - Ornstein-Uhlenbeck SDEs, where explicit calculations may be made for the postinterventiondistributions.Chapter 9 concerns identiability of the mixing matrix in ICA. It is a well-knownresult that identiability of the mixing matrix depends crucially on whether theerror distributions are Gaussian or not. We attempt to elucidate what happens inthe case where the error distributions are close to but not exactly Gaussian.Finally, Chapter 10 discusses degrees of freedom in nonlinear regression. Our motivatingproblem is that of L1-constrained and L1-penalized estimation in nonlinearregression. Our objective is to obtain results leading to the calculation of the degreesof freedom of an estimator in order to enable sparse model selection by optimalchoice of the penalization parameter. We prove two results related to the degrees offreedom, one theoretical result for constrained estimation, and one more practicallyapplicable for L1-penalized estimation.

AB - Ornstein-Uhlenbeck SDEs, where explicit calculations may be made for the postinterventiondistributions.Chapter 9 concerns identiability of the mixing matrix in ICA. It is a well-knownresult that identiability of the mixing matrix depends crucially on whether theerror distributions are Gaussian or not. We attempt to elucidate what happens inthe case where the error distributions are close to but not exactly Gaussian.Finally, Chapter 10 discusses degrees of freedom in nonlinear regression. Our motivatingproblem is that of L1-constrained and L1-penalized estimation in nonlinearregression. Our objective is to obtain results leading to the calculation of the degreesof freedom of an estimator in order to enable sparse model selection by optimalchoice of the penalization parameter. We prove two results related to the degrees offreedom, one theoretical result for constrained estimation, and one more practicallyapplicable for L1-penalized estimation.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122333045405763

M3 - Ph.D. thesis

SN - 978-87-7078-386-6

BT - On Martingales, Causality, Identifiability and Model Selection

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -