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A probability density function estimation using F-transform. (English) Zbl 1194.62030
Summary: 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 I. Perfilieva [Fuzzy Sets Syst. 157, No. 8, 993–1023 (2006; Zbl 1092.41022)]. 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 E. Parzen windows [Ann. Math. Stat. 33, 1065–1076 (1962; Zbl 0116.11302)]. Such an approach can be of a great value, mainly when dealing with financial data, i.e., large samples of observations.

62G07 Density estimation
62G86 Nonparametric inference and fuzziness
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