Higher-order asymptotic theory of shrinkage estimation for general statistical models

Hiroshi Shiraishi, Masanobu Taniguchi, Takashi Yamashita

    Research output: Contribution to journalArticle


    In this study, we develop a higher-order asymptotic theory of shrinkage estimation for general statistical models, which includes dependent processes, multivariate models, and regression models (i.e., non-independent and identically distributed models). We introduce a shrinkage estimator of the maximum likelihood estimator (MLE) and compare it with the standard MLE by using the third-order mean squared error. A sufficient condition for the shrinkage estimator to improve the MLE is given in a general setting. Our model is described as a curved statistical model p(⋅;θ(u)), where θ is a parameter of the larger model and u is a parameter of interest with dimu<dimθ. This setting is especially suitable for estimating portfolio coefficients u based on the mean and variance parameters θ. We finally provide the results of our numerical study and discuss an interesting feature of the shrinkage estimator.

    Original languageEnglish
    Pages (from-to)198-211
    Number of pages14
    JournalJournal of Multivariate Analysis
    Publication statusPublished - 2018 Jul 1


    • Curved statistical model
    • Dependent data
    • Higher-order asymptotic theory
    • Maximum likelihood estimation
    • Portfolio estimation
    • Regression model
    • Shrinkage estimator
    • Stationary process

    ASJC Scopus subject areas

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

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