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Abstract:
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We consider the problem of statistical classification with functional predictors when part(s) of the curve may be missing. Here, missingness can appear in both the data and the new observation to be classified. Furthermore, the popular Missingness at Random (MAR) assumption used in the literature is not warranted for our setup and will not be imposed. We derive a representation for the theoretically optimal classifier for the current missing functional predictor setup. Given a random sample (the data), we also propose a rather easy to implement kernel-type classification rule and study the asymptotic optimality (Bayes consistency) of our proposed classifier under a number of assumptions.
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