Title :
H2/H∞ approach to the histogram method for density estimation
Author :
Nagahara, M. ; Sato, K.I. ; Yamamoto, Y.
Author_Institution :
Grad. Sch. of Inf., Kyoto Univ., Kyoto, Japan
Abstract :
In this paper, we study nonparametric density estimation by the histogram method. Histogram is interpreted as quantization, which decreases the amount of information. Then interpolation (or estimation) of the missing information is needed. To achieve this, we introduce sampled-data H2/Hinfin optimization. We design the reconstruction system which optimizes the worst case error between the original PDF and the estimation. The optimization is formulated by linear matrix inequalities and equalities. Numerical examples are illustrated to show effectiveness of our method.
Keywords :
Hinfin optimisation; interpolation; linear matrix inequalities; nonparametric statistics; quantisation (signal); sampled data filters; signal reconstruction; statistical distributions; PDF; histogram method; interpolation; linear matrix equality; linear matrix inequality; nonparametric density estimation; probability distribution; quantization; reconstruction system design; sampled-data H2/Hinfin optimization; worst case error; Control theory; Design optimization; Filters; Frequency; Histograms; Informatics; Interpolation; Optimization methods; Quantization; Symmetric matrices; Density estimation; histogram method; sampled-data control;
Conference_Titel :
ICCAS-SICE, 2009
Conference_Location :
Fukuoka
Print_ISBN :
978-4-907764-34-0
Electronic_ISBN :
978-4-907764-33-3
