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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Anticipated and Adaptive Prediction in Functional Discriminant Analysis
verfasst von : Cristian Preda, Gilbert Saporta, Mohamed Hadj Mbarek
Erschienen in: Proceedings of COMPSTAT'2010
Verlag: Physica-Verlag HD
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Linear discriminant analysis with binary response is considered when the predictor is a functional random variable
$$X=\{X_{t},t\in [0,T]\}$$
,
$$T \in\mathbb{R}$$
. Motivated by a food industry problem, we develop a methodology to anticipate the prediction by determining the smallest
$$T^{*}$$
,
$$T^{*} \leq T$$
, such that
$$X^{*} = \{X_{t}, t\in [0,T^{*}]\}$$
and
X
give similar predictions. The adaptive prediction concerns the observation of a new curve
ω
on
$$[0, T^{*}(\omega)]$$
instead of [0,
T
] and answers to the question “How long should we observe
ω
(
$$T^{*}(\omega)=?$$
) for having the same prediction as on [0,
T
] ?”. We answer to this question by defining a conservation measure with respect to the class the new curve is predicted.