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Asymptotic theory of parameter estimation by a contrast function based on interpolation error

  • Yoshihiro Suto
  • Yan LiuEmail author
  • Masanobu Taniguchi
Article

Abstract

Interpolation is an important issue for a variety fields of statistics (e.g., missing data analysis). In time series analysis, the best interpolator for missing points problem has been investigated in several ways. In this paper, the asymptotics of a contrast function estimator defined by pseudo interpolation error for stationary process are investigated. We estimate parameters of the process by minimizing the pseudo interpolation error written in terms of a fitted parametric spectral density and the periodogram based on observed stretch. The estimator has the consistency and asymptotical normality. Although the criterion for the interpolation problem is known as the best in the sense of smallest mean square error for past and future extrapolation, it is shown that the estimator is asymptotically inefficient in general parameter estimation, which leads to an unexpected result.

Keywords

Interpolation error Contrast function Spectral density  Stationary process Periodogram Asymptotic efficiency 

Notes

Acknowledgments

The authors are grateful to the editor and three anonymous referees for their careful reading and constructive comments.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Pure and Applied MathematicsWaseda UniversityTokyoJapan

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