Estimation of Star-Shaped Distributions
AbstractScatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the star-generalized radius density, we consider a non-parametric kernel-type estimator. This estimator is combined with a parametric estimator for the contours which are assumed to follow a parametric model. Therefore, the semiparametric procedure features the ﬂexibility of nonparametric estimators and the simple estimation and interpretation of parametric estimators. Alternatively, we consider pure parametric estimators for the density. For the semiparametric density estimator, we prove rates of uniform, almost sure convergence which coincide with the corresponding rates of one-dimensional kernel density estimators when excluding the center of the distribution. We show that the standardized density estimator is asymptotically normally distributed. Moreover, the almost sure convergence rate of the estimated distribution function of the star-generalized radius is derived. A particular new two-dimensional distribution class is adapted here to agricultural and ﬁnancial data sets. View Full-Text
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Liebscher, E.; Richter, W.-D. Estimation of Star-Shaped Distributions. Risks 2016, 4, 44.
Liebscher E, Richter W-D. Estimation of Star-Shaped Distributions. Risks. 2016; 4(4):44.Chicago/Turabian Style
Liebscher, Eckhard; Richter, Wolf-Dieter. 2016. "Estimation of Star-Shaped Distributions." Risks 4, no. 4: 44.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.