Testing a Regression Model when we Have Smooth Alternatives in Mind
AbstractGoodness-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.
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Bibliographic InfoPaper provided by Catholique de Louvain - Institut de statistique in its series Papers with number 9808.
Length: 21 pages
Date of creation: 1998
Date of revision:
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Postal: Universite Catholique de Louvain, Institut de Statistique, Voie du Roman Pays, 34 B-1348 Louvain- La-Neuve, Belgique.
TESTING ; MODELS;
Other versions of this item:
- Wolfgang Härdle, 1999. "Testing a Regression Model When We Have Smooth Alternatives in Mind," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 26(2), pages 221-238.
- Haerdle,Wolfgang & Kneip,Alois, 1992. "Testing aregression model when we have smooth alternatives in mind," Discussion Paper Serie A 389, University of Bonn, Germany.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
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- Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
- Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
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