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Testing a Regression Model When We Have Smooth Alternatives in Mind

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  • Wolfgang Härdle
  • Alois Kneip

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 χ2‐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.

Suggested Citation

  • Wolfgang Härdle & Alois Kneip, 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, June.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:2:p:221-238
    DOI: 10.1111/1467-9469.00146
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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.

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