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

Yoshihiro Suto, Yan Liu, Masanobu Taniguchi

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    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.

    Original languageEnglish
    Pages (from-to)93-110
    Number of pages18
    JournalStatistical Inference for Stochastic Processes
    Volume19
    Issue number1
    DOIs
    Publication statusPublished - 2016 Apr 1

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    Keywords

    • Asymptotic efficiency
    • Contrast function
    • Interpolation error
    • Periodogram
    • Spectral density
    • Stationary process

    ASJC Scopus subject areas

    • Statistics and Probability

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