Testing a regression model when we have smooth alternatives in mind
(1999) Scandinavian Journal of Statistics : theory and applications — Vol. 26, n° 2, p. 221-238 (1999)
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- 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 chi(2)-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.
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Citations
Hardle, W., & Kneip, A. (1999). Testing a regression model when we have smooth alternatives in mind. Scandinavian Journal of Statistics : theory and applications, 26(2), 221-238. https://doi.org/10.1111/1467-9469.00146 (Original work published 1999)