Data-Driven Lack-of-Fit Tests for General Parametric Models
In this chapter we consider testing the fit of parametric models of a more general nature than the constant mean model of Chapter 7. We begin with the case of a linear model, i.e., the case where r is hypothesized to be a linear combination of known functions. The fit of such models can be tested by applying the methods of Chapter 7 to residuals. It will be argued that test statistics generally have the same distributions they had in Chapter 7 if least squares is used to estimate model parameters.
KeywordsFourier Coefficient Null Distribution Multivariate Normal Distribution Local Polynomial Pivotal Quantity
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