Dimension spectra for multifractal measures with connections to nonparametric density estimation
We consider relations between Rényi's and Hentschel - Procaccia's definitions of generalized dimensions of a probability measure μ, and give conditions under which the two concepts are equivalent/different. Estimators of the dimension spectrum are developed, and strong consistency is established. Particular cases of our estimators are methods based on the sample correlation integral and box counti
