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

Yoshihiro Suto, Yan Liu, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    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

    Fingerprint

    Interpolation Error
    Asymptotic Theory
    Parameter Estimation
    Estimator
    Periodogram
    Interpolation Problem
    Time Series Analysis
    Spectral Density
    Stationary Process
    Stretch
    Missing Data
    Extrapolation
    Mean square error
    Normality
    Data analysis
    Interpolate
    Statistics
    Estimate

    Keywords

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

    ASJC Scopus subject areas

    • Statistics and Probability

    Cite this

    Asymptotic theory of parameter estimation by a contrast function based on interpolation error. / Suto, Yoshihiro; Liu, Yan; Taniguchi, Masanobu.

    In: Statistical Inference for Stochastic Processes, Vol. 19, No. 1, 01.04.2016, p. 93-110.

    Research output: Contribution to journalArticle

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