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Title: Partially and dependently observed functional data Authors:  Stefan Rameseder - Regensburg (Germany) [presenting]
Dominik Liebl - University Bonn (Germany)
Abstract: As in the case of missing data in uni- and multivariate data sets, without assuming the so-called ``missing-at-random'' condition it is generally impossible to consistently estimate, e.g. the mean-function, if functional data are only partially observed. By contrast, for functional data there is a chance to consistently estimate the mean-function even though the ``missing-at-random'' assumption is violated. By using a detour via the fundamental theorem of calculus, we propose a new estimator of the mean-function for partially observed functional data. While we theoretically compare bias and variance of our estimator with typical mean estimators, we additionally perform an extended two-part simulation study. On the one hand, we investigate the applicability of our estimator via an identification procedure by sequential testing. On the other hand, we consider bias and variance of our estimator versus other estimators in different missing data scenarios. As an empirical motivation, we apply this procedure onto supply curves in a frequential multi-unit auction with pay-as-bid pricing mechanism and exogenous and predetermined demand. In this market design, typical trading strategies strongly depend on the preannounced demand for which our estimator in opposite to others delivers useful results for the whole mean curve.