Testing a Regression Model When We Have Smooth Alternatives in Mind

Wolfgang Härdle and Alois Kneip

Scandinavian Journal of Statistics, 1999, vol. 26, issue 2, 221-238

Abstract: Goodness‐of‐fit tests based on residual sums of squares are standard procedures used when fitting regression models. Often we have a smooth alternative in mind, a qualitative feature that the χ2‐test does not take into account. We show that the power of detecting a smooth alternative increases when we smooth the current model as well. The proposed test is shown to be able to detect any continuous local alternative tending to zero slower than n−1/2. Theoretical results also address minimax non‐parametric hypothesis testing in Sobolev spaces. A simulation study is presented, and the procedure is applied to expenditure curve estimation.

Date: 1999
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