Generalized log-gamma additive partial linear models with P-spline smoothing

In this paper additive partial linear models with generalized log-gamma errors and P-spline smoothing are proposed for uncensored data. This class derived from the generalized gamma distribution contains various continuous asymmetric distributions to the right and to the left with domain on the real line and has the normal distribution as a particular case. The location parameter is modeled in a semiparametric way so that one has a generalized gamma accelerated failure time additive partial linear model. A joint iterative process is derived, that combines the penalized Fisher scoring algorithm for estimating the parametric and nonparametric regression coefficients and a quasi-Newton procedure for obtaining the scale and shape estimates. Discussions on the inferential aspects of the former estimators as well as on the derivation of the effective degrees of freedom are given. Diagnostic procedures are also proposed, such as residual analysis and sensitivity studies based on the local influence approach. Simulation studies are performed to assess the empirical distributions of the parametric and nonparametric estimators and a real data set on personal injury insurance claims made in Australia from January 1998 to June 1999 is analyzed by the methodology developed through the paper. Technical results, tables, graphs, R codes and the data set used in the application are presented as Supplementary Materials.

Automated summary

This paper introduces the additive partial linear models with generalized log-gamma errors and P-spline smoothing for uncensored data. The models are able to fit various continuous asymmetric distributions, including the normal distribution, using a semiparametric approach. A joint iterative process is derived to estimate the regression coefficients, and diagnostic procedures are proposed for residual analysis and sensitivity studies. Simulation studies and the analysis of a real data set demonstrate the effectiveness of the proposed methodology.