Penalized maximum likelihood estimation for generalized linear point processes

Publikation: Working paper › Forskning

Standard

Penalized maximum likelihood estimation for generalized linear point processes. / Hansen, Niels Richard.

2010.

Publikation: Working paper › Forskning

Harvard

Hansen, NR 2010 'Penalized maximum likelihood estimation for generalized linear point processes'.

APA

Hansen, N. R. (2010). Penalized maximum likelihood estimation for generalized linear point processes.

Vancouver

Hansen NR. Penalized maximum likelihood estimation for generalized linear point processes. 2010 mar. 3.

Author

Hansen, Niels Richard. / Penalized maximum likelihood estimation for generalized linear point processes. 2010.

Bibtex

@techreport{1c89677014f54a188e09f9cf7cce164a,
title = "Penalized maximum likelihood estimation for generalized linear point processes",
abstract = "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.",
keywords = "math.ST, math.PR, stat.ME, stat.TH",
author = "Hansen, {Niels Richard}",
year = "2010",
month = mar,
day = "3",
language = "English",
type = "WorkingPaper",

}

RIS

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