Second order optimality for estimators in time series regression models

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    We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator over(β, ^) proposed by Hannan [Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, pp. 17-37]. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of over(β, ^). Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that over(β, ^) has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of over(β, ^). Numerical studies are given to confirm the theoretical results.

    元の言語English
    ページ(範囲)638-659
    ページ数22
    ジャーナルJournal of Multivariate Analysis
    98
    発行部数3
    DOI
    出版物ステータスPublished - 2007 3

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    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Numerical Analysis
    • Statistics and Probability

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