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Approximate standard errors in semiparametric models.

M Durban1, C A Hackett, I D Currie

  • 1Biomathematics and Statistics Scotland, Scottish Crop Research Institute, Invergowrie, Dundee, Scotland.

Biometrics
|April 21, 2001
PubMed
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This study introduces a faster, approximate method for calculating standard errors in semiparametric regression models. The new approach simplifies complex computations, offering accurate results for smoothing splines and loess methods.

Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Semiparametric regression models are widely used in statistical analysis.
  • Estimating regression coefficients and their standard errors is crucial for inference.
  • The back-fitting algorithm provides estimates but calculating standard errors is computationally intensive.

Purpose of the Study:

  • To develop a computationally less demanding method for calculating standard errors of regression coefficients in semiparametric models.
  • To provide an alternative to the computationally intensive exact calculation.

Main Methods:

  • Derivation of an explicit expression for regression coefficient estimates using the back-fitting algorithm.
  • Development and presentation of an approximate method for calculating standard errors.
  • Assessment of the approximation's adequacy using smoothing splines and loess methods.

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Main Results:

  • An explicit expression for back-fitting estimates is obtained.
  • A less demanding approximate method for standard error calculation is presented.
  • The method is exact for smoothing splines and provides good estimates for loess.

Conclusions:

  • The proposed approximate method significantly reduces the computational burden for standard error calculation in semiparametric models.
  • The approximation is validated for its accuracy with common smoothing techniques.
  • This facilitates more efficient statistical inference in semiparametric modeling.