Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter

Hassan Pazira*, Luigi Augugliaro, Ernst Wit

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
301 Downloads (Pure)

Abstract

A large class of modeling and prediction problems involves outcomes that belong to an exponential family distribution. Generalized linear models (GLMs) are a standard way of dealing with such situations. Even in high-dimensional feature spaces GLMs can be extended to deal with such situations. Penalized inference approaches, such as the or SCAD, or extensions of least angle regression, such as dgLARS, have been proposed to deal with GLMs with high-dimensional feature spaces. Although the theory underlying these methods is in principle generic, the implementation has remained restricted to dispersion-free models, such as the Poisson and logistic regression models. The aim of this manuscript is to extend the differential geometric least angle regression method for high-dimensional GLMs to arbitrary exponential dispersion family distributions with arbitrary link functions. This entails, first, extending the predictor-corrector (PC) algorithm to arbitrary distributions and link functions, and second, proposing an efficient estimator of the dispersion parameter. Furthermore, improvements to the computational algorithm lead to an important speed-up of the PC algorithm. Simulations provide supportive evidence concerning the proposed efficient algorithms for estimating coefficients and dispersion parameter. The resulting method has been implemented in our R package (which will be merged with the original dglars package) and is shown to be an effective method for inference for arbitrary classes of GLMs.

Original languageEnglish
Pages (from-to)753-774
Number of pages22
JournalStatistics and Computing
Volume28
Issue number4
Early online date21-Jun-2017
DOIs
Publication statusPublished - Jul-2018

Keywords

  • High-dimensional inference
  • Generalized linear models
  • Least angle regression
  • Predictor-corrector algorithm
  • Dispersion paremeter
  • LEAST ANGLE REGRESSION
  • LINEAR-MODELS
  • VARIABLE SELECTION
  • CROSS-VALIDATION
  • DANTZIG SELECTOR
  • SHRINKAGE

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