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Testing a Regression Model When We Have Smooth Alternatives in Mind

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  • Wolfgang Härdle

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.
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Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:2:p:221-238
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    Cited by:

    1. 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.
    2. 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.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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