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Asymptotic confidence intervals in ridge regression based on the Edgeworth expansion

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Abstract

Ridge Regression techniques have been found useful to reduce mean square errors of parameter estimates when multicollinearity is present. But the usefulness of the method rest not only upon its ability to produce good parameter estimates, with smaller mean squared error than Ordinary Least Squares, but also on having reasonable inferential procedures. The aim of this paper is to develop asymptotic confidence intervals for the model parameters based on Ridge Regression estimates and the Edgeworth expansion. Some simulation experiments are carried out to compare these confidence intervals with those obtained from the application of Ordinary Least Squares. Also, an example will be provided based on the well known data set of Hald.

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ciencias, Universidad del Bío Bío, Avda. Collao 1202, Casilla 5C, Concepción, Chile

    Luis Firinguetti

  2. Departamento de Matemática y C.C., Facultad de Ciencia, Universidad de Santiago, Alameda Libertador Bernardo O’Higgins, 3363, Santiago, Chile

    Gladys Bobadilla

Authors
  1. Luis Firinguetti
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  2. Gladys Bobadilla
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Corresponding author

Correspondence to Luis Firinguetti.

Additional information

This work was supported by FONDECYT-Chile, Grant #1010009 and DICYT, Grant # 49931BA.

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Firinguetti, L., Bobadilla, G. Asymptotic confidence intervals in ridge regression based on the Edgeworth expansion. Stat Papers 52, 287–307 (2011). https://doi.org/10.1007/s00362-009-0229-5

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  • DOI: https://doi.org/10.1007/s00362-009-0229-5

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