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Mean quadratic error of an estimate of splines of first order in a model of linear regression

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Abstract

We study the mean quadratic error of an estimate of splines of the first order, which is obtained by the method of least squares under the assumption that the data represents a superposition of proper values of a spline and a white noise. A quantitative formula for the quadratic mean error is found and its asymptotics is investigated.

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Literature cited

  1. G. A. F. Seber, Linear Regression Analysis, Wiley, New York (1977).

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  2. Yu. S. Zav'yalov, B. I. Kvasov, and V. L. Miroshnichenko, The Methods of Spline-Functions, [in Russian], Nauka, Moscow (1980).

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  3. I. V. Proskuryakov, Problems in Linear Algebra [in Russian], Gostekhteorizdat, Moscow (1957).

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of Ukrainian SSR, Kiev

    M. Yu. Petunina

Authors
  1. M. Yu. Petunina
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 429–432, March, 1991.

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Petunina, M.Y. Mean quadratic error of an estimate of splines of first order in a model of linear regression. Ukr Math J 43, 395–397 (1991). https://doi.org/10.1007/BF01670084

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  • DOI: https://doi.org/10.1007/BF01670084

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