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- W4229752777 abstract "A method of solving normal equations $X'X{bf b} = X'{bf y}$ in the linear model not of full rank is to apply a convenient set of linear restrictions $C{bf b} = {bf c}$, where C is complementary to $X',X$ and ${bf c}$ is usually ${bf 0}$ A characterization is derived of all generalized inverses of $X'X$ which produce the solution subject to $C{bf b} = {bf 0}$. This leads to the finding that the $g_3 $-inverse of X subject to $CX^{g_3 } = 0$ is unique and to the complementary result that $C^{g_3 } $ subject to $XC^{g_3 } = 0$ is unique. A case is made on this basis for discarding Plackett’s matrix $D[ 7 ]$, which appears in some books. A general formula is derived for obtaining the solution under one set of restrictions from that under a different set. The set of left inverses of $[ {begin{array}{*{20}c} X C end{array} } ]$, where C has full row-rank, is considered." @default.
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- W4229752777 date "1976-11-01" @default.
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- W4229752777 title "Some Aspects of the Solution of Singular Normal Equations with the Use of Linear Restrictions" @default.
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- W4229752777 doi "https://doi.org/10.1137/0131038" @default.
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