Histogram density estimators based upon a fuzzy partition

This paper presents a density estimator based upon a histogram computed on a fuzzy partition. We prove the consistency of this estimator in the Mean Squared Error (MSE). We give the optimal bin width of the estimator which minimizes the Asymptotic Integrated Mean Squared Error (AIMSE).

[1]  D. W. Scott.  On optimal and data based histograms , 1979 .

[2]  Jonathan Lawry,et al.  Classification of Weather Radar Images using Linguistic Decision Trees with Conditional Labelling , 2007, 2007 IEEE International Fuzzy Systems Conference.

[3]  Uzay Kaymak,et al.  Fuzzy histograms: A Statistical Analysis , 2005, EUSFLAT Conf..

[4]  Kevin Loquin,et al.  Fuzzy Histograms and Density Estimation , 2006, SMPS.

[5]  David W. Scott,et al.  Multivariate Density Estimation: Theory, Practice, and Visualization , 1992, Wiley Series in Probability and Statistics.

[6]  Walter F. Willcox,et al.  Contributions to the History of Statistics. , 1933 .

[7]  Olivier Strauss,et al.  Rough histograms for robust statistics , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[8]  D. W. Scott,et al.  Kernel density estimation with binned data , 1985 .

[9]  Uzay Kaymak,et al.  Probabilistic and statistical fuzzy set foundations of competitive exception learning , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[10]  Thomas A. Runkler.  Fuzzy histograms and fuzzy chi-squared tests for independence , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).