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On leastp-th power methods in multiple regressions and location estimations

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Abstract

The solution of the matricial systemZ=HX+V is derived. The observations are given by the matrixZ(n×m) and arem-components vectors. The parameter matrix isH(n×g), whileX(g×m) is the unknown andV(n×m) the residual matrix. The solutionX is estimated in order to minimize anL p -norm ofV defined with the help of anL r -norm on theV rows. The minimization algorithm is a steepest descent method with a specially chosen step size to “avoid” the singularities. The general problem shrinks in simple regression or location problems whilem org is reduced to the unit.

Possibly more important is the recursive solution of this same general problem; a solutionX (n) being obtained, we require the solutionX (n+1) of the same system plus one row. In this context the productHX can be seen as a filtered version of the originalZ. The inversion of a system ofg linear equations is required at each step of the recursive solution.

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  1. MBLE Research Laboratory, 2, Avenue Van Becelaere, B-1170, Brussels, Belgium

    W. Rey

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  1. W. Rey
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Rey, W. On leastp-th power methods in multiple regressions and location estimations. BIT 15, 174–184 (1975). https://doi.org/10.1007/BF01932691

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  • DOI: https://doi.org/10.1007/BF01932691

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