Construction Of A Conservative Confidence Region From Projections Of An Exact Confidence Region In Multiple Linear-Regression

    Authors

    D. M. Nickerson

    Comments

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    Abbreviated Journal Title

    Am. Stat.

    Keywords

    BONFERRONI; SCHEFFE; WORKING-HOTELLING; Statistics & Probability

    Abstract

    The problem of constructing a confidence region for simultaneously estimating p, p greater-than-or-equal-to 2, linear regression parameters for which confidence statements can be made on the individual parameters is revisited. Here, an intercept may be included among the p paremeters. The technique is due to Working and Hotelling (1929) and Scheffe (1959) and uses the p separate projections of the exact (1 - alpha) 100% confidence ellipsoid (ellipse if p = 2) to give confidence intervals for each regression parameter. The Cartesian product of these p confidence intervals gives a p-dimensional rectangle that contains the confidence ellipsoid and hence has a joint confidence coefficient of at least (1 - alpha). A simple calculus proof is given to determine these projections. The projection procedure is compared with the Bonferroni procedure for this case.

    Journal Title

    American Statistician

    Volume

    48

    Issue/Number

    2

    Publication Date

    1-1-1994

    Document Type

    Article

    Language

    English

    First Page

    120

    Last Page

    124

    WOS Identifier

    WOS:A1994NU49900022

    ISSN

    0003-1305

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