Robust estimation in partially nonlinear models

DANIELA RODRIGUEZ

Guayaquil

Congreso; ICORS International Conference on Robust Statistics; 2019

Statistical inference for multidimensional random variables commonly focuses onfunctionals of its distribution that are either purely parametric or purely nonparametric.A reasonable parametric model produces precise inferences, while a badly misspecifed model possibly leads to seriously misleading conclusions.In the partially nonlinear regression model, one observes the response variable $y$ obeying the model:$$y = \eta(t)+g(x,\beta) +\varepsilon$$where $(x,t)$ is a vector of explanatory variables, $g$ is a prespecified function, $\beta$ is avector of unknown true parameters to be estimated, $\eta$ is an unknow true smooth function to be estimared and $\varepsilon$ is a random error.The partially nonlinear model, retains the flexibility of nonparametric models and the interpretability of nonlinear parametric models. As special cases of partially nonlinear models, partially linear models are popular in the literature.In this talk, we introduce robust estimates for the parametric and nonparametric components for the partially nonlinear model. The proposed estimators are based on a three step procedure. We show some asymptotic properties such as that the consistent of both estimatores and the asymptotic distribution of the estimators of the parametric component. Also, we study the behaviour of the proposal, through a Monte Carlostudy where we compare the performance of our estimators with that of the classical ones. We illustrated our proposal with a real dataset.