Article
Full entry |
PDF
(0.6 MB)
Feedback
PDF
(0.6 MB)
Feedback
Keywords:
fuzzy transform; probability density function estimation; smoothing filter; financial returns
fuzzy transform; probability density function estimation; smoothing filter; financial returns
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 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.
References:
[1] Ahalt, S. C., Krishnamurthy, A. K., Chen, P. K., Melton, D. E.: Competative learning algorithms for vector quantization. Neural Networks 4 (1993), 3, 277 – 290.
[2] Assenza, A., Valle, M., Verleysen, M.: A comparative study of various probabilty density estimation methods for data analysis. Internat. J. Comput. Intell. Systems 1 (2009), 2, 188–201.
[3] Fan, J., Yao, Q.: Nonlinear Time Series: Nonparametric and Parametric Methods. (Springer Series in Statistics.) Springer-Verlag, Berlin 2005. MR 1964455 | Zbl 1014.62103
[4] Härdle, W., Müller, M., Sperlich, S., Werwatz, A.: Nonparametric and Semiparametric Models. Springer-Verlag, New York 2004. MR 2061786
[5] Kostelich, E. J., Yorke, J. A.: Noise reduction: Finding the simplest dynamical system consistent with the data. Physica D 41 (1990), 183–196. MR 1049125 | Zbl 0705.58036
[6] Kuo, Hui-Hsiung: White Noise Distribution Theory. CRC Press, 1996. MR 1387829 | Zbl 0853.60001
[7] McLachlan, G. J., Peel, D.: Finite Mixture Models. Wiley, New York 2000. MR 1789474 | Zbl 0963.62061
[8] Nachtegael, M., Weken, D. Van der, Ville, D. Van De, Kerre, E. E., eds.: Fuzzy Filters for Image Processing. (Studies in Fuzziness and Soft Computing.) Springer-Verlag, 2003.
[9] Parzen, E.: On estimation of a probabilty density function and mode. Ann. Math. Statist. 33 (1962), 1065–1076. DOI 10.1214/aoms/1177704472 | MR 0143282
[10] Perfilieva, I.: Fuzzy transforms: Theory and applications. Fuzzy Sets and Systems 157 (2006), 8, 993–1023. MR 2218243 | Zbl 1092.41022
[11] Perfilieva, I., Valášek, R.: Fuzzy transforms in removing noise. In: Innovation in Hybrid Intelligent Systems. Springer-Verlag, Berlin – Heidelberg 2005.
[12] Silverman, B. W.: Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC, London 1986. MR 0848134 | Zbl 0617.62042
[13] Simonoff, J. S.: Smoothing Methods in Statistics. Springer-Verlag, New York 1996. MR 1391963 | Zbl 0859.62035
[14] Stefanini, L.: Fuzzy transforms and smooth function. In: Proc. IFSA/EUSFLAT 2009, Lisabon 2009.
Search
Partner of
