Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection

Shuzhuan Zheng; Rong Liu; Lijian Yang; Wolfgang K. Härdle

Ayuda

Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection

Shuzhuan Zheng ^[1] ; Rong Liu ^[2] ; Lijian Yang ^[3] ; Wolfgang K. Härdle ^[4]
1. [1] Soochow University
  
  Soochow University
  
  China
2. [2] University of Toledo
  
  University of Toledo
  
  City of Toledo, Estados Unidos
3. [3] Tsinghua University
  
  Tsinghua University
  
  China
4. [4] Humboldt University of Berlin
  
  Humboldt University of Berlin
  
  Berlin, Stadt, Alemania
Mostrar afiliaciones +
Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 25, Nº. 4, 2016, págs. 607-626
Idioma: inglés
DOI: 10.1007/s11749-016-0480-8
Texto completo no disponible (Saber más ...)
Resumen
- In spite of widespread use of generalized additive models (GAMs) to remedy the “curse of dimensionality”, there is no well-grounded methodology developed for simultaneous inference and variable selection for GAM in existing literature. However, both are essential in enhancing the capability of statistical models. To this end, we establish simultaneous confidence corridors (SCCs) and a type of Bayesian information criterion (BIC) through the spline-backfitted kernel smoothing techniques proposed in recent articles. To characterize the global features of each non-parametric components, SCCs are constructed for testing their overall trends and entire shapes. By extending the BIC in additive models with identity/trivial link, an asymptotically consistent BIC approach for variable selection is built up in GAM to improve the parsimony of model without loss of prediction accuracy. Simulations and a real example corroborate the above findings.