Partially linear beta regression model with autoregressive errors
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Guillermo Ferreira [1] ; Jorge I. Figueroa-Zúñiga [1] ; Mário de Castro [2]
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[1] Universidad de Concepción
Universidad de Concepción
Comuna de Concepción, Chile
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[2] Universidade de São Paulo
Universidade de São Paulo
Brasil
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 24, Nº. 4, 2015, págs. 752-775
- Idioma: inglés
- DOI: 10.1007/s11749-015-0433-7
- Texto completo no disponible (Saber más ...)
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Resumen
This paper is focused on developing a methodology to deal with time series data on the unit interval modeled by a partially linear model with correlated disturbances from a Bayesian perspective. In this context, the linear predictor of the beta regression model incorporates an unknown smooth function with time as an auxiliary covariate and a set of regressors. In addition, an autoregressive dependence structure is proposed for the errors of the model. This formulation can capture the dynamic evolution of curves using both non-stochastic explanatory variables and non-parametric components, allowing an accurate fit with a limited number of parameters. Diagnostic measures are derived from the case-deletion approach and an influence measure based on the Kullback–Leibler divergence is studied and thus, a new method to determine the optimal order of the autoregressive processes through an adaptive procedure using the conditional predictive ordinate statistic is presented. A simulation study is conducted to assess some properties of the Bayesian estimator. Finally, the proposed methodology is illustrated in two real-life applications.
