Naslov
Assessment of the Effective Rank of a (Co)variance Matrix : A Non-parametric Goodness-of-fit Test

Autori
Tomišić, Vladislav ; Simeon, Vladimir

Izvornik
Journal of chemometrics (0886-9383) 7 (1993), 5; 381-392

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Factor analysis; Kolmogorov-Smirnov test; Non-parametric tests in factor analysis; Non-parametric tests for principal components; Principal component analysis

Sažetak
Each eigenvector of the dispersion matrix [X]T [X] was shown to be a partial predictor of the original data matrix [X], the sum of the predictions from the individual principal components being equal to the expectance of [X]. By comparing the distributions of the members of two neighbouring predicted matrices, [X̃]1…i and [X̃]1…i+1 (i.e. the sums of the first i and i + 1 individual predictions respectively), it was shown that they should be indistinguishable provided that i is equal to or greater than the effective rank of [X], and significantly different otherwise. This was confirmed by analysing the visible absorption spectra of methyl orange and methyl red solutions as well as the Raman spectra of Na2SO4 and MgSO4 solutions. On the grounds of these findings, a non-parametric goodness-of-fit test for assessing the effective rank of [X] was proposed which proved to be comparatively conservative and more robust than most currently used tests.

Izvorni jezik
Engleski

Znanstvena područja
Kemija

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