Model robust regression: Combining parametric, nonparametric, and semiparametric methods

The proper combination of parametric and nonparametric regression procedure s can improve upon the shortcomings of each when used individually. Conside red is the situation where the researcher has an idea of which parametric m odel should explain the behavior of the data, but this model is not adequat e throughout the entire range of the data. An extension of partial linear r egression and two other methods of model-robust regression are developed an d compared in this context. The model-robust procedures each involve the pr oportional mixing of a parametric fit to the data and a nonparametric fit t o either the data or residuals. Asymptotically optimal estimates for the mi xing parameters are given, along with their convergence rates. Performance is based on bias and variance considerations, and theoretical mean squared error formulas are used to compare procedures. Simulation results establish the accuracy of the theoretical formulas and illustrate the potential bene fits of the model-robust procedures. Two examples are given: Example 1 uses generated data from an underlying model with defined misspecification to s how the theoretical benefits of the model-robust procedures., and Example 2 supplies an interesting application.