Estimation of order-restricted means of two normal populations under the LINEX loss function

Tie Feng Ma, Shuangzhe LIU

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    In this paper, the estimation of order-restricted means of two normal distributions is studied under the LINEX loss function, when the variances are unknown and possibly unequal. Under certain sufficient conditions to be described in this paper, the proposed plug-in estimators uniformly perform better than the existing unrestricted maximum likelihood estimators. Further, the restricted maximum likelihood estimators are compared with the unrestricted maximum likelihood estimators under the Pitman nearness criterion. A simulation study is conducted and it is shown that our proposed plug-in estimators perform better than the unrestricted maximum likelihood estimators. An illustrative example of real data analysis is also given to compare the estimators
    Original languageEnglish
    Pages (from-to)409-425
    Number of pages17
    JournalMetrika
    Volume76
    Issue number76
    DOIs
    Publication statusPublished - 2013

    Fingerprint

    LINEX Loss Function
    Normal Population
    Plug-in Estimator
    Maximum Likelihood Estimator
    Restricted Maximum Likelihood Estimator
    Unequal
    Gaussian distribution
    Data analysis
    Simulation Study
    Estimator
    Unknown
    Sufficient Conditions
    Loss function
    Maximum likelihood estimator

    Cite this

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    title = "Estimation of order-restricted means of two normal populations under the LINEX loss function",
    abstract = "In this paper, the estimation of order-restricted means of two normal distributions is studied under the LINEX loss function, when the variances are unknown and possibly unequal. Under certain sufficient conditions to be described in this paper, the proposed plug-in estimators uniformly perform better than the existing unrestricted maximum likelihood estimators. Further, the restricted maximum likelihood estimators are compared with the unrestricted maximum likelihood estimators under the Pitman nearness criterion. A simulation study is conducted and it is shown that our proposed plug-in estimators perform better than the unrestricted maximum likelihood estimators. An illustrative example of real data analysis is also given to compare the estimators",
    keywords = "Isotonic estimator, LINEX loss, Order-restricted means, Pitman nearness criterion",
    author = "Ma, {Tie Feng} and Shuangzhe LIU",
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    language = "English",
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    Estimation of order-restricted means of two normal populations under the LINEX loss function. / Ma, Tie Feng; LIU, Shuangzhe.

    In: Metrika, Vol. 76, No. 76, 2013, p. 409-425.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Estimation of order-restricted means of two normal populations under the LINEX loss function

    AU - Ma, Tie Feng

    AU - LIU, Shuangzhe

    PY - 2013

    Y1 - 2013

    N2 - In this paper, the estimation of order-restricted means of two normal distributions is studied under the LINEX loss function, when the variances are unknown and possibly unequal. Under certain sufficient conditions to be described in this paper, the proposed plug-in estimators uniformly perform better than the existing unrestricted maximum likelihood estimators. Further, the restricted maximum likelihood estimators are compared with the unrestricted maximum likelihood estimators under the Pitman nearness criterion. A simulation study is conducted and it is shown that our proposed plug-in estimators perform better than the unrestricted maximum likelihood estimators. An illustrative example of real data analysis is also given to compare the estimators

    AB - In this paper, the estimation of order-restricted means of two normal distributions is studied under the LINEX loss function, when the variances are unknown and possibly unequal. Under certain sufficient conditions to be described in this paper, the proposed plug-in estimators uniformly perform better than the existing unrestricted maximum likelihood estimators. Further, the restricted maximum likelihood estimators are compared with the unrestricted maximum likelihood estimators under the Pitman nearness criterion. A simulation study is conducted and it is shown that our proposed plug-in estimators perform better than the unrestricted maximum likelihood estimators. An illustrative example of real data analysis is also given to compare the estimators

    KW - Isotonic estimator

    KW - LINEX loss

    KW - Order-restricted means

    KW - Pitman nearness criterion

    U2 - 10.1007/s00184-012-0396-6

    DO - 10.1007/s00184-012-0396-6

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    JF - Metrika

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