135622
20181007231114.0
10.5075/epfl-thesis-4386
doi
urn:nbn:ch:bel-epfl-thesis4386-9
urn
5756342
nebis
THESIS_LIB
eng
4386
Robust inference for generalized linear models
binary and poisson regression
Lausanne
2009
EPFL
2009
183
Theses
Generalized Linear Models have become a commonly used tool of data analysis. Such models are used to fit regressions for univariate responses with normal, gamma, binomial or Poisson distribution. Maximum likelihood is generally applied as fitting method. In the usual regression setting the least absolute-deviations estimator (L1-norm) is a popular alternative to least squares (L2-norm) because of its simplicity and its robustness properties. In the first part of this thesis we examine the question of how much of these robustness features carry over to the setting of generalized linear models. We study a robust procedure based on the minimum absolute deviation estimator of Morgenthaler (1992), the Lq quasi-likelihood when q = 1. In particular, we investigate the influence function of these estimates and we compare their sensitivity to that of the maximum likelihood estimate. Furthermore we particularly explore the Lq quasi-likelihood estimates in binary regression. These estimates are difficult to compute. We derive a simpler estimator, which has a similar form as the Lq quasi-likelihood estimate. The resulting estimating equation consists in a simple modification of the familiar maximum likelihood equation with the weights wq(μ). This presents an improvement compared to other robust estimates discussed in the literature that typically have weights, which depend on the couple (xi, yi) rather than on μi = h(xiT β) alone. Finally, we generalize this estimator to Poisson regression. The resulting estimating equation is a weighted maximum likelihood with weights that depend on μ only.
Robustness
Generalized linear models
Binary regression
Poisson regression
Maximum quasi-likelihood
Robustesse
Modèles linéaires généralisés
Régression binaire
Régression de Poisson
Maximum quasi-vraisemblance
Hosseinian, Sahar
Morgenthaler, Stephan
dir.
105911
241889
Texte intégral / Full text
3831525
Texte intégral / Full text
http://infoscience.epfl.ch/record/135622/files/EPFL_TH4386.pdf
STAP
252209
U10127
oai:infoscience.tind.io:135622
SB
DOI
thesis
thesis-bn2018
DOI2
SB
IMA
EDMA
STAP
2009
4386/THESES
EPFL
PUBLISHED
THESIS