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Testing goodness of fit of polynomial models via spline smoothing techniques. (English) Zbl 0793.62026
Summary: A new test statistic is proposed for testing goodness of fit of an \(m\)-th order polynomial regression model. The test statistic is \[ \int^ 1_ 0 \biggl[ \mu_ \lambda^{(m)} (t) \biggr]^ 2 \text{d}t, \] where \(\mu_ \lambda^{(m)}\) is the \(m\)-th order derivative of a \(2m\)-th order smoothing spline estimator for the regression function \(\mu\) and \(\lambda\) is its associated smoothing parameter. The large sample properties of the test statistic are derived under both the null hypothesis and local alternatives. A numerical example is included that illustrates the technique.

MSC:
62G10 Nonparametric hypothesis testing
62J02 General nonlinear regression
62G07 Density estimation
62E20 Asymptotic distribution theory in statistics
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