Residuals and their statistical properties in symmetrical nonlinear models

In this work we present theoretical details of a general residual for symmetric nonlinear regression models. This class of models includes all symmetric continuous distributions such as normal, Student-t, Pearson VII, power exponential and logistic. Such regression models are used for the analysis of data sets containing influential or outlying observations, that can significantly influence inferential conclusions. On the basis of expansions of Cox and Snell [Cox, D.R., Snell, E.J., 1968. A general definition of residuals. Journal of the Royal Statistical Society B 30, 248-275], we calculate first and second moments of a general definition of a residual for symmetrical nonlinear regression models. Also, the statistical properties of some proposed residuals are studied using Monte Carlo simulations for the Michaelis-Menten model, frequently used in chemical and biological experiments.