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Quadratic deviation of penalized mean squares regression estimates

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  • Doukhan, Paul
  • Gassiat, Elisabeth

Abstract

Our aim in this work is to give a global test of hypothesis concerning the smoothing spline estimate of a regression function. For this, we prove a central limit theorem for integrated squares of such estimates. That leads to a test whose confidence sets are either continuous or discrete L2-balls. We consider the case of nonperiodic splines and the periodic splines for which we get explicit expressions of the constants involved in such a test.

Suggested Citation

  • Doukhan, Paul & Gassiat, Elisabeth, 1992. "Quadratic deviation of penalized mean squares regression estimates," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 89-101, April.
    • Handle: RePEc:eee:jmvana:v:41:y:1992:i:1:p:89-101
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