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We propose a general framework for the construction and analysis of minimax estimators for a wide class of functionals of discrete distributions, where the alphabet size S is unknown and may be scaling with the number of observations n. We treat the respective regions where the functional is " nonsmooth " and " smooth " separately. In the " nonsmooth "(More)
We refine the general methodology in [1] for the construction and analysis of essentially minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions with support size S comparable with the number of observations n. Specifically, we determine the " smooth " and " non-smooth "(More)
Location-aware networks are of great importance and interest in both commercial and security applications. This paper determines the localization accuracy of the agent in a wireless network, where the agent is equipped with an antenna array ranging with several anchor nodes in a far-field environment. In view of the Cramér-Rao bound, we derive based on(More)
C lassifying images and identifying objects in images is a challenging task in many applications such as image retrieval or annotation. Recent research increasingly relies on the bag-of-words (BoW) representation and its corresponding learning model because this representation has generated promising results in various vision tasks including image and(More)
We consider estimating the Shannon entropy of a discrete distribution P from n i.i.d. samples. Recently, Jiao, Venkat, Han, and Weissman (JVHW), and Wu and Yang constructed approximation theoretic estimators that achieve the minimax L<sub>2</sub> rates in estimating entropy. Their estimators are consistent given n &#x226B; S/lnS samples, where S is the(More)
Maximum likelihood is the most widely used statistical estimation technique. Recent work by Jiao, Venkat, Han, and Weissman [1] introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements-both in theory and in practice-over the maximum likelihood estimator (MLE), particularly in(More)
The Dirichlet prior is widely used in estimating discrete distributions and functionals of discrete distributions. In terms of Shannon entropy estimation, one approach is to plug-in the Dirichlet prior smoothed distribution into the entropy functional, while the other one is to calculate the Bayes estimator for entropy under the Dirichlet prior for squared(More)
—The free-space optical (FSO) communications can achieve high capacity with huge unlicensed optical spectrum and low operational costs. The corresponding performance analysis of FSO systems over turbulence channels is very limited, especially when using multiple apertures at both transmitter and receiver sides. This paper aim to provide the ergodic capacity(More)