Testing a Regression Model when we Have Smooth Alternatives in Mind

W. Hardle and A. Kneip

Working Papers from Catholique de Louvain - Institut de statistique

Abstract: Goodness-of-fit tests based on residual sum of squares are a standard procedure in fitiing regression models. Often we have a smooth alternative in mind, a qualitative feature that the X2-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 nonparametric hypothesis testing in Sobolev spaces.

Keywords: TESTING; MODELS (search for similar items in EconPapers)
JEL-codes: C12 (search for similar items in EconPapers)
Pages: 21 pages
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:fth:louvis:9808

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