B1002
Title: Highly robust and efficient negative binomial regression
Authors: Michael Amiguet - University of Lausanne (Switzerland)
Victor Yohai - Universidad de Buenos Aires (Argentina)
Alfio Marazzi - University of Lausanne (Switzerland) [presenting]
Abstract: We consider the regression model $Y | x \sim F_{\mu (x),\alpha}$, where $F_{\mu,\alpha}$ is the negative binomial distribution with $\mu(x) = E(Y|x) = h(\beta^{\text{T}} x)$ and dispersion $\alpha$; $x$ is a covariate vector, $\beta$ a vector of coefficients, $h$ a link function. Given a sample $(y_i,x_i)$, we are looking for highly robust and efficient estimators of $\beta$ and $\alpha$ based on three steps. In the first step the maximum rank correlation estimator is used to consistently estimate the slopes up to a scale factor. The scale factor, the intercept, and the dispersion parameter are consistently estimated using a combination of M-estimates. In the second step, outliers are identified observing that, if $u_i$ is uniformly distributed, then the tail probabilities $F_{\mu (x_i),\alpha}(y_i)-u_i f_{\mu (x_i) ,\alpha }(y_i)$ are uniformly distributed ($f_{\mu,\alpha}$ is the density of $F_{\mu,\alpha}$). For the final step, an adaptation of the adaptively truncated maximum likelihood regression estimate is used.
