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Title: An R package for Cramer-von Mises goodness-of-fit tests in regression models Authors:  Sandie Ferrigno - INRIA NANCY / University Nancy Lorraine (France) [presenting]
Marie-Jose Martinez - University of Grenoble (France)
Romain Azais - INRIA Nancy (France)
Abstract: Let $Y=m(X)+\sigma(X)\varepsilon$ be a regression model, where $m(\cdot)$ is the regression function, $\sigma^{2}(\cdot)$ the variance function and $\varepsilon$ the random error term. Methods to assess how well a model fits a set of observations fall under the banner of goodness-of-fit tests. Many tests have been developed to assess the different assumptions for this kind of model. Most of them are ``directional'' in that they detect departures from mainly a given assumption of the model. Other tests are ``global'' in that they assess whether a model fits a data set on all its assumptions. We focus on the task of choosing the structural part $m(\cdot)$. It gets most attention because it contains easily interpretable information about the relationship between $X$ and $Y$. To valid the form of the regression function, we consider three nonparametric tests based on a generalization of the Cram\'er-von Mises statistic. The first two are directional tests, while the third is a global test. To perform these goodness-of-fit tests based on a generalization of the Cram\'er-von Mises statistic, we have developed a R package providing an easy-to-use tool for many users. The use of the package is illustrated using simulated to compare the three implemented tests.