Empirical Comparison of the Classification Performance of Robust Linear and Quadratic Discriminant Analysis

Robust estimators under a functional common principal components model

“…. , d. Hence, the proposed estimators 20 are qualitatively robust and consistent. In particular, the estimators are robust if the populations are independent each with 21 an elliptical distribution E (µ 1 , 1 ) × · · · × E (µ k , k ) such that, for some i = 1, .…”

“…In particular, the intercondylar notch is considered important by medical specialists. We refer to Ramsay 20 and Silverman (2002) for details. The data set consists of N = 96 notch outlines, on each of which we have some concomitant 21 information which provides evidence of arthritic bone damage.…”

“…Table 4 Values of 1000 ×  λ i,j with  λ i,j = s 2 i,n i (  φ f ,m ) and s i,n i the standard deviation or the M-scale estimator. different robust quadratic discrimination is always preferred to robust linear discrimination, see Joossens and Croux (2004).…”

“…Each of the three populations is contaminated with a contaminating distribution highly concentrated on the fourth 20 principal direction denoted C 4,ϵ as in Section 5.1. In this framework, the contaminated observations denoted X…”

“…Let φ j stand for the eigenfunctions of the covariance operator 1 related to the covariance kernel γ 1 (s, t) and let Bi(1, ϵ) 20 be the Bernoulli distribution with probability of success ϵ. For each model, a contamination in the fourth eigenfunction was 21 considered and denoted C 4,ϵ , where ϵ corresponds to the contamination level.…”