Robust nonlinear regression: 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 scale exponential convex model is appropriate for carbon dioxide data because besides having smaller standard errors of parameter estimates and smaller residual standard errors, it is numerically stable. Due to large range of data that goes 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.

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