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fuzzy transform; probability density function estimation; smoothing filter; financial returns
The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method of Parzen windows. Such an approach can be of a great value mainly when dealing with financial data, i. e. large samples of observations.
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