Robust estimators in a generalized partly linear regression model under mononicity constraints

BOENTE, GRACIELA; RODRIGUEZ, DANIELA; VENA, PABLO

Pisa

Conferencia; 7th International Conference of the ERCIM WG on Computational and Methodological Statistics (ERCIM 2014); 2014

ERCIM Working Group on Computational and Methodological Statistics (CMStatistics) and the University of Pisa

The situation in which the observations follow an isotonic generalized partly linear model is considered. Under this model, the mean of the responses is modeled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component, and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance or Pearson residuals. The empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. We investigate the performance of the estimators through a Monte Carlo study for the Binomial and Gamma families of distributions.