Prakash Patil (University of Birmingham)
Smoothing based Lack-of-Fit (or Goodness-of-Fit) Tests

To construct a nonparametric (smoothing-based) test of lack-of-fit, one measures one way or other, the discrepancy between a smooth estimator of the unknown curve and the hypothesised curve. Although there are many possible choices for measuring this discrepancy, for being technically most easy to deal with, the lack-of-fit tests based on the ISE seem to have received the most(?) attention. But since a test based on the ISE requires the estimation of the unknown curve, its ability to distinguish between the null model and the departures from the null model is linked to the smoothing parameter that one chooses to estimate the curve. Whereas, if one takes a local view and then constructs a test, one can show that the test has better power properties. And although the performance of the test is still linked to the smoothing parameter, the choice of smoothing parameter will now be dictated by the `testing’ aspect of the problem rather than be driven by the estimation of the unknown curve. In this talk, we will mainly use regression quantile curves to illustrate the above points but will show that this procedure could be used for density and hazard rate curves. More…