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Multivariate density estimation by probing depth. (English) Zbl 0919.62050

Dodge, Yadolah (ed.), \(L_1\)-statistical procedures and related topics. Papers of the 3rd international conference on \(L_1\) norm and related methods held in Neuchâtel, Switzerland, August 11–15, 1997. Hayward, CA: IMS, Institute of Mathematical Statistics. IMS Lect. Notes, Monogr. Ser. 31, 415-430 (1997).
Summary: In high dimension, the estimation of a density is difficult because the observed data gets increasingly sparse with the dimension. This is known as the curse of dimensionality. For that reason, in high dimension, universally consistent estimators such as the kernel density estimator are not practical. We consider a class of multivariate densities, within which a density function \(f\) can be expressed as \(f=g\circ D\) for some given notion of data depth \(D\) and some real function \(g\). We propose a density estimator which is shown to be consistent within the class, and it converges at the same rate as the univariate kernel density estimator.
For the entire collection see [Zbl 0882.00044].

MSC:

62H12 Estimation in multivariate analysis
62G07 Density estimation
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