000			01644nab a22002777a 4500
001			G69019
003			MX-TxCIM
005			20230516180721.0
008			121211b |||p||p||||||| |z||| |
022			_a1467-9868
022			_a1369-7412 (Online)
040			_aMX-TxCIM
041			_aeng
090			_aREP-175
100	1		_aGabriel, K. R _9496
245	0	1	_aLeast squares approximation of matrices by additive and multiplicative models
260			_c1978. _aUnited Kingdom : _bWiley,
340			_aComputer File|Printed
520			_aReduced rank approximation of matrices by Householder–Young methods is shown to be equivalent to fitting of a bilinear (multiplicative) model and to projection onto an optimally chosen subspace. The relation to linear approximation is made evident. Least squares fitting of a mixed linear (additive) and bilinear (multiplicative) model is proved to be a two-stage process: (1) fit the linear part of the model, then take residuals, and (2) fit the bilinear part to the residuals. Extensions of this result are given as well as some results on distributions of residuals and tests against alternatives of given rank. Statistical applications are shown in principal component analysis, in biplot graphical display and in fitting additive or Mandel-type models to two-way tables.
546			_aText in English
650		7	_2AGROVOC _930836 _aLeast squares method
650		7	_2AGROVOC _917216 _aComponents
650		7	_2AGROVOC _92624 _aStatistical methods
773	0		_tJournal of the Royal Statistical Society Series B _gv. 40, no. 2, p. 186-196 _dUnited Kingdom : Wiley, 1978. _x1467-9868
942			_cJA _2ddc
999			_c19668 _d19668