On an elliptical thin-plate spline partially varying-coefficient model

Magaly S. Moraga, Germán Ibacache-Pulgar, Orietta Nicolis

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this work, we study the thin-plate spline partially varying-coefficient models with elliptical contoured errors in order to allow distributions with heavier and lighter tails than the normal ones, such as logistic, Pearson VII, power exponential, and Student-t, to be considered. We develop an estimation process for the parameters of the model based on the doubly penalized likelihood function and using smoothing splines. In addition, an explicit conditional solution for the double penalized maximum likelihood estimators is derived to obtain closed expressions for the variance-covariance matrix of the estimators, effective degrees of freedom of the smooth functions and surfaces, and hat matrix associated with the model. To show the proposed methodology, we analyze the Boston housing data utilizing-plate spline partially varying-coefficient model with normal and Student-t errors. This analysis suggests that the proposed model is helpful when we want to describe the effect of some covariates that vary smoothly as a function of other covariates, geographic referencing, and data with heavy-tailed indications.

Original languageEnglish
Pages (from-to)205-228
Number of pages24
JournalChilean Journal of Statistics
Issue number2
Publication statusPublished - Dec 2021


  • Maximum doubly penalized likelihood estimates
  • Partially varying-coefficient models
  • Robust estimates
  • Thin-plate spline models

ASJC Scopus subject areas

  • Statistics and Probability


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