GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.
نویسندگان
چکیده
We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on ℝ. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n-2/5 when -1 < s < ∞ where s = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of s-concave densities with s < -1.
منابع مشابه
GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES BY CHARLES R. DOSS
R d is log-concave if p = e where φ :Rd → [−∞,∞) is concave. We denote the class of all such densities p on R by Pd,0. Log-concave densities are always unimodal and have convex level sets. Furthermore, log-concavity is preserved under marginalization and convolution. Thus, the classes of log-concave densities can be viewed as natural nonparametric extensions of the class of Gaussian densities. ...
متن کاملGLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES BY CHARLES
R d is log-concave if p = e where φ :Rd → [−∞,∞) is concave. We denote the class of all such densities p on R by Pd,0. Log-concave densities are always unimodal and have convex level sets. Furthermore, log-concavity is preserved under marginalization and convolution. Thus, the classes of log-concave densities can be viewed as natural nonparametric extensions of the class of Gaussian densities. ...
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ورودعنوان ژورنال:
- Annals of statistics
دوره 44 3 شماره
صفحات -
تاریخ انتشار 2016