A comparison of nonlinear and nonparametric regression methods

Chen, Min (2010) A comparison of nonlinear and nonparametric regression methods. Masters thesis, Memorial University of Newfoundland.

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Abstract

In this report, we investigate the performance of nonlinear regression and nonparametric regression with data set simulated under a nonlinear parametric model. First, we consider the nonlinear least squares estimation method for the model. Then, we apply various nonparametric regression methods such as kernel methods, spline smoothing, and wavelet version of estimators with the same model. The nonlinear least squares estimation method produces the best estimation in terms of MSE among all the regression methods. Both kernel methods and wavelet version of estimation methods produce reasonably small values of MSE. Moreover, the wavelet regression method performances best among all the nonparametric methods. The spline method produces unacceptably large MSE due to large variance of estimation. The boundary issues do exist in all the nonparametric regression methods due to less density of data points.

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