Covariance matrix and transfer function of dynamic generalized linear models

Statistical inference for dynamic generalized linear models (DGLMs) is challenging due to the time varying nature of the unknown parameters in these models. In this paper, we focus on the covariance matrix and the transfer function, the two key components in DGLMs. We first establish some convergence results for the covariance matrix estimation. We then provide an in-depth study of the transfer function on its stability and Fourier transformation, which is necessary for parameter estimation in DGLMs. Implications of our results on estimation in DGLMs are illustrated in the paper through a simulation study and a real data example. Our understanding on DGLMs has substantially improved though this study.

[1]  Guangbao Guo,et al.  Parallel tempering for dynamic generalized linear models , 2016 .

[2]  K. Triantafyllopoulos.  Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal , 2009 .

[3]  Jesse Windle,et al.  Dynamic Generalized Linear Models , 2012 .

[4]  Monica Chiogna,et al.  Dynamic generalized linear models with application to environmental epidemiology , 2002 .

[5]  M. West,et al.  Dynamic Generalized Linear Models and Bayesian Forecasting , 1985 .

[6]  Guangbao Guo,et al.  Parallel Statistical Computing for Statistical Inference , 2012 .

[7]  Kathryn B. Laskey,et al.  Population Markov Chain Monte Carlo , 2004, Machine Learning.

[8]  Philippe Lambert,et al.  Dynamic generalized linear models and repeated measurements , 1995 .

[9]  Marco A. R. Ferreira,et al.  Transfer functions in dynamic generalized linear models , 2010 .

[10]  D. Gamerman.  Markov chain Monte Carlo for dynamic generalised linear models , 1998 .

[11]  L. Fahrmeir.  Posterior Mode Estimation by Extended Kalman Filtering for Multivariate Dynamic Generalized Linear Models , 1992 .

[12]  L. Fahrmeir,et al.  Penalized likelihood estimation and iterative Kalman smoothing for non-Gaussian dynamic regression models , 1997 .

[13]  Alexandra M. Schmidt,et al.  An efficient sampling scheme for dynamic generalized models , 2013, Computational Statistics.

[14]  D. Dey,et al.  On Dynamic Generalized Linear Models with Applications , 2013 .

[15]  Wei Shao,et al.  An efficient proposal distribution for Metropolis-Hastings using a B-splines technique , 2013, Comput. Stat. Data Anal..

[16]  Kostas Triantafyllopoulos,et al.  Convergence of Discount Time Series Dynamic Linear Models , 2007 .