James-Stein estimators for time series regression models

Motohiro Senda, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    The least squares (LS) estimator seems the natural estimator of the coefficients of a Gaussian linear regression model. However, if the dimension of the vector of coefficients is greater than 2 and the residuals are independent and identically distributed, this conventional estimator is not admissible. James and Stein [Estimation with quadratic loss, Proceedings of the Fourth Berkely Symposium vol. 1, 1961, pp. 361-379] proposed a shrinkage estimator (James-Stein estimator) which improves the least squares estimator with respect to the mean squares error loss function. In this paper, we investigate the mean squares error of the James-Stein (JS) estimator for the regression coefficients when the residuals are generated from a Gaussian stationary process. Then, sufficient conditions for the JS to improve the LS are given. It is important to know the influence of the dependence on the JS. Also numerical studies illuminate some interesting features of the improvement. The results have potential applications to economics, engineering, and natural sciences.

    Original languageEnglish
    Pages (from-to)1984-1996
    Number of pages13
    JournalJournal of Multivariate Analysis
    Volume97
    Issue number9
    DOIs
    Publication statusPublished - 2006 Oct

    Fingerprint

    James-Stein Estimator
    Least Squares Estimator
    Time Series Models
    Mean square error
    Time series
    Regression Model
    Stein Estimation
    Quadratic Loss
    Estimator
    Stationary Gaussian Process
    Shrinkage Estimator
    Natural sciences
    Error function
    Coefficient
    Regression Coefficient
    Loss Function
    Linear Regression Model
    Linear regression
    Identically distributed
    Least Squares

    Keywords

    • Gaussian stationary process
    • James-Stein estimator
    • Least squares estimator
    • Mean squares error
    • Regression spectrum
    • Residual spectral density matrix
    • Time series regression model

    ASJC Scopus subject areas

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

    Cite this

    James-Stein estimators for time series regression models. / Senda, Motohiro; Taniguchi, Masanobu.

    In: Journal of Multivariate Analysis, Vol. 97, No. 9, 10.2006, p. 1984-1996.

    Research output: Contribution to journalArticle

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