Multivariate Statistical Modelling Based on Generalized Linear Models

By Eric R. Ziegel. Technometrics, 2002

1,013 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cb44fb606a3c3ea6146b8e5689edcc11ac0f7190

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Citations in the corpus

Generating and Calibrating Probabilistic Quantitative Precipitation Forecasts from the High-Resolution NWP Model COSMO-DE (2012, methodology): “LR and the mixture models are special cases of generalized linear models (GLMs; McCullagh and Nelder 1998; Fahrmeir and Tutz 1994) which are briefly described in the following.”
A Bayesian Semiparametric Latent Variable Model for Mixed Responses (2007, neutral): “For more information on ordinal modelling we refer to Fahrmeir and Tutz (2001), or Johnson and Albert (1999).”
Partial Likelihood Inference For Time Series Following Generalized Linear Models (2004, methodology): “Generalized linear models as introduced by Nelder and Wedderburn (1972) and further treated in McCullagh and Nelder (1989) (see also Fahrmeir and Tutz, 2001), resolve these problems when the observations follow a distribution from an exponential family, rendering the classical linear model under…”
Regression analysis of variates observed on (0, 1): percentages, proportions and fractions (2003, background): “Because the beta distribution is a member of the exponential class of distributions, these maximum likelihood estimators have all the statistical properties established for maximum likelihood estimators for this class of distributions (see Jorgensen (1983) or Fahrmeir and Tutz (1994) for further dis”
On the statistical and theoretical basis of signal detection theory and extensions: Unequal variance, random coefficient, and mixture models (2010, background): “…ordinal responses, one should not simply allow each criterion, ck, to be (independently) random, because the assumption of strict ordering of the criteria can then be violated, as has been recognized in statistics (e.g., see Fahrmeir & Tutz, 2001) and in psychology (e.g. Rosner & Kochanski, 2009).”
Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis (2009, background): “With regard to the analysis of the polio data, the detection of a decreasing trend has been a classical issue (See Chan and Ledolter, 1995; Kuk and Cheng, 1997; Jorgensen et al., 1999; Fahrmeir and Tutz, 1994; Davis et al., 2000).”
Gaussian Processes for Ordinal Regression (2005, methodology): “First, the additive models (Fahrmeir and Tutz, 2001) are defined by functions in each input dimension, whereas the GPs can have more general non-additive covariance functions; second, the kernel trick allows to use infinite basis function expansions; third, the GPs perform Bayesian inference in the ”
Count Time Series: A Methodological Review (2021, background): “Early textbooks on the topic are Fahrmeir and Tutz (2001) and Kedem and Fokianos (2002).”
Geoadditive Survival Models (2006, background): “The first case leads to the piecewise exponential model, and the integral reduces to a sum (see Fahrmeir and Tutz 2001, sec.”
Generalized additive models for location, scale and shape (2005, methodology): “An approximate EM algorithm was used by Fahrmeir and Tutz (2001), pages 298–303, and by Diggle et al. (2002), pages 172–175, to estimate hyperparameters in GLMMs and is similarly applied here to maximize approximately over λ the marginal likelihood of λ, L.λ/ (or equivalently the posterior marginal…”
Hierarchical Insurance Claims Modeling (2008, methodology): “One approach to modeling this data set would be to use techniques from multivariate longitudinal data (see, e.g., Fahrmeir and Tutz 2001); however, as we have pointed out, in most years policyholders do not incur a claim, resulting in many repeated 0’s (see, e.g., Olsen and Shafer 2001), and when a…”
Dynamic factor analysis to estimate common trends in fisheries time series (2003, methodology): “Various diagnostic tools to check the residuals for violations of these assumptions are presented in Harvey (1989), Fahrmeir and Tutz (1994), and Durbin and Koopman (2001).”
Monotonic Regression Based on Bayesian P–Splines (2008, background): “GAMs assume that, given xn and vn, the response yn follows an exponential family distribution (Hastie and Tibshirani 1990; Fahrmeir and Tutz 2001) p(yn|xn, vn) = c(yn, θn) exp { ynθn − b(θn) φ } and that the mean µn = E(yn|xn, vn) is linked to a semiparametric additive predictor ηn via a known link…”
A scalable modular convex solver for regularized risk minimization (2007, methodology): “…regression [37], ordinal regression [21], ranking [15], maximization of multivariate performance measures [24], structured estimation [38, 40], Gaussian Process regression [43], conditional random ﬁelds [28], graphical models [14], exponential families [3], and generalized linear models [17].”
Parameter Change Test for Poisson Autoregressive Models (2014, methodology): “With regard to the analysis of the polio data, the detection of a decreasing trend has been a classical issue among researchers (Zeger, 1988; Chan & Ledolter, 1995; Kuk & Cheng, 1997; Davis et al., 2000; Fahrmeir & Tutz, 2001; Davis & Wu, 2009).”
Applying Generalized Linear Models (2000, background): “Several important and well-known books on generalized linear models are available (Aitkin et al., 1989; McCullagh and Nelder, 1989; Dobson, 1990; Fahrmeir and Tutz, 1994); the present book is intended to be complementary to them.”