Penalized maximum likelihood estimation for generalized linear point processes
Publikation: Working paper › Forskning
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Penalized maximum likelihood estimation for generalized linear point processes. / Hansen, Niels Richard.
2010.Publikation: Working paper › Forskning
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TY - UNPB
T1 - Penalized maximum likelihood estimation for generalized linear point processes
AU - Hansen, Niels Richard
PY - 2010/3/3
Y1 - 2010/3/3
N2 - A generalized linear point process is specified in terms of an intensity that depends upon a linear predictor process through a fixed non-linear function. We present a framework where the linear predictor is parametrized by a Banach space and give results on Gateaux differentiability of the log-likelihood. Of particular interest is when the intensity is expressed in terms of a linear filter parametrized by a Sobolev space. Using that the Sobolev spaces are reproducing kernel Hilbert spaces we derive results on the representation of the penalized maximum likelihood estimator in a special case and the gradient of the negative log-likelihood in general. The latter is used to develop a descent algorithm in the Sobolev space. We conclude the paper by extensions to multivariate and additive model specifications. The methods are implemented in the R-package ppstat.
AB - A generalized linear point process is specified in terms of an intensity that depends upon a linear predictor process through a fixed non-linear function. We present a framework where the linear predictor is parametrized by a Banach space and give results on Gateaux differentiability of the log-likelihood. Of particular interest is when the intensity is expressed in terms of a linear filter parametrized by a Sobolev space. Using that the Sobolev spaces are reproducing kernel Hilbert spaces we derive results on the representation of the penalized maximum likelihood estimator in a special case and the gradient of the negative log-likelihood in general. The latter is used to develop a descent algorithm in the Sobolev space. We conclude the paper by extensions to multivariate and additive model specifications. The methods are implemented in the R-package ppstat.
KW - math.ST
KW - math.PR
KW - stat.ME
KW - stat.TH
M3 - Working paper
BT - Penalized maximum likelihood estimation for generalized linear point processes
ER -
ID: 135496696