Testing aregression 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 University of Bonn, Germany in its series Discussion Paper Serie A with number 389.
Date of creation: Dec 1992
Date of revision:
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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
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Regression models; Goodness-of-fit-test; Smooth alternatives;
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.
- Hardle, W. & Kneip, A., 1998. "Testing a Regression Model when we Have Smooth Alternatives in Mind," Papers 9808, Catholique de Louvain - Institut de statistique.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
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- 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.
- 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.
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