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

Hiroshi Shiraishi, Masanobu Taniguchi, Takashi Yamashita

    Research output: Contribution to journalArticle

    Abstract

    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
    Volume166
    DOIs
    Publication statusPublished - 2018 Jul 1

    Fingerprint

    Shrinkage Estimation
    Higher-order Asymptotics
    Shrinkage Estimator
    Asymptotic Theory
    Maximum Likelihood Estimator
    Statistical Model
    Maximum likelihood
    Multivariate Regression
    Multivariate Models
    Mean Squared Error
    Identically distributed
    Numerical Study
    Regression Model
    Model
    Dependent
    Sufficient Conditions
    Coefficient
    Shrinkage estimation
    Maximum likelihood estimator
    Asymptotic theory

    Keywords

    • 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

    Cite this

    Higher-order asymptotic theory of shrinkage estimation for general statistical models. / Shiraishi, Hiroshi; Taniguchi, Masanobu; Yamashita, Takashi.

    In: Journal of Multivariate Analysis, Vol. 166, 01.07.2018, p. 198-211.

    Research output: Contribution to journalArticle

    @article{e828c209937746b0b98ca5f1f9c564e3,
    title = "Higher-order asymptotic theory of shrinkage estimation for general statistical models",
    abstract = "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",
    keywords = "Curved statistical model, Dependent data, Higher-order asymptotic theory, Maximum likelihood estimation, Portfolio estimation, Regression model, Shrinkage estimator, Stationary process",
    author = "Hiroshi Shiraishi and Masanobu Taniguchi and Takashi Yamashita",
    year = "2018",
    month = "7",
    day = "1",
    doi = "10.1016/j.jmva.2018.03.006",
    language = "English",
    volume = "166",
    pages = "198--211",
    journal = "Journal of Multivariate Analysis",
    issn = "0047-259X",
    publisher = "Academic Press Inc.",

    }

    TY - JOUR

    T1 - Higher-order asymptotic theory of shrinkage estimation for general statistical models

    AU - Shiraishi, Hiroshi

    AU - Taniguchi, Masanobu

    AU - Yamashita, Takashi

    PY - 2018/7/1

    Y1 - 2018/7/1

    N2 - 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

    AB - 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

    KW - Curved statistical model

    KW - Dependent data

    KW - Higher-order asymptotic theory

    KW - Maximum likelihood estimation

    KW - Portfolio estimation

    KW - Regression model

    KW - Shrinkage estimator

    KW - Stationary process

    UR - http://www.scopus.com/inward/record.url?scp=85044596010&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85044596010&partnerID=8YFLogxK

    U2 - 10.1016/j.jmva.2018.03.006

    DO - 10.1016/j.jmva.2018.03.006

    M3 - Article

    AN - SCOPUS:85044596010

    VL - 166

    SP - 198

    EP - 211

    JO - Journal of Multivariate Analysis

    JF - Journal of Multivariate Analysis

    SN - 0047-259X

    ER -