Hossein Riazoshams: Robust Nonlinear Regression, Inference and computational problems: Case study for modeling the greenhouse gases, Methane and Carbon Dioxide concentration in atmosphere

Four nonlinear regression models are proposed for the atmospheric carbon dioxide and methane gas concentrations data, reported by United Nation 1989. Among those considered, the Exponential with Intercept is the most preferred one to model methane data due to better convergence and lower correlation between parameters. On the other hand, the Scaled Exponential and Exponential with intercept model are appropriate for carbon dioxide data because besides having smaller standard errors of parameter estimates and smaller residual standard errors, it is numerically stable, meanwhile the power model although is difficult to attain the convergence but (only) graphically fit better. Due to large range of data that back to history to 7000 years ago, there is a big dispersion in data set, so that it made us to apply robust nonlinear regression estimation methods to have a smoother model.