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
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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.
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