Algorithm for Vector Autoregressive Model Parameter Estimation Using an Orthogonalization Procedure

2002 ◽  
Vol 30 (2) ◽  
pp. 260-271 ◽  
Author(s):  
Epifanio Bagarinao ◽  
Shunsuke Sato
Keyword(s):  
Parameter Estimation ◽  
Autoregressive Model ◽  
Vector Autoregressive Model ◽  
Vector Autoregressive ◽  
Model Parameter ◽  
Model Parameter Estimation ◽  
Orthogonalization Procedure

scholarly journals A Spatial Panel Structural Vector Autoregressive Model with Interactive Effects and Its Simulation

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 883
Author(s):  
Yaqing Liu ◽  
Hongbing Ouyang ◽  
Xiaolu Wei
Keyword(s):  
Autoregressive Model ◽  
Common Factors ◽  
Interactive Effects ◽  
Vector Autoregressive Model ◽  
Finite Sample ◽  
Vector Autoregressive ◽  
Spatial Panel ◽  
The Common ◽  
Structural Vector Autoregressive Model ◽  
Structural Vector

The existing spatial panel structural vector auto-regressive model can effectively capture the time and spatial dynamic dependence of endogenous variables. However, the hypothesis that the common factors have the same effect for all spatial units is unreasonable. Therefore, incorporating time effects, spatial effects, and time-individual effects, this paper develops a more general spatial panel structural vector autoregressive model with interactive effects (ISpSVAR) that can reflect the different effects of common factors on different spatial units. Additionally, based on whether or not the common factors can be observed, this paper proposes procedures to estimate ISpSVAR separately and studies the finite sample properties of estimators by Monte Carlo simulation. The simulation results show the effectiveness of the proposed ISpSVAR model and its estimation procedures.

l2-Penalized temporal logit-mixed models for the estimation of regional obesity prevalence over time

2021 ◽  
pp. 096228022110175
Author(s):  
Jan P Burgard ◽  
Joscha Krause ◽  
Ralf Münnich ◽  
Domingo Morales
Keyword(s):  
Parameter Estimation ◽  
Medical Treatment ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Obesity Prevalence ◽  
Model Parameter ◽  
Model Parameter Estimation ◽  
Public Health Reporting ◽  
Over Time

Obesity is considered to be one of the primary health risks in modern industrialized societies. Estimating the evolution of its prevalence over time is an essential element of public health reporting. This requires the application of suitable statistical methods on epidemiologic data with substantial local detail. Generalized linear-mixed models with medical treatment records as covariates mark a powerful combination for this purpose. However, the task is methodologically challenging. Disease frequencies are subject to both regional and temporal heterogeneity. Medical treatment records often show strong internal correlation due to diagnosis-related grouping. This frequently causes excessive variance in model parameter estimation due to rank-deficiency problems. Further, generalized linear-mixed models are often estimated via approximate inference methods as their likelihood functions do not have closed forms. These problems combined lead to unacceptable uncertainty in prevalence estimates over time. We propose an l2-penalized temporal logit-mixed model to solve these issues. We derive empirical best predictors and present a parametric bootstrap to estimate their mean-squared errors. A novel penalized maximum approximate likelihood algorithm for model parameter estimation is stated. With this new methodology, the regional obesity prevalence in Germany from 2009 to 2012 is estimated. We find that the national prevalence ranges between 15 and 16%, with significant regional clustering in eastern Germany.

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