The problem of distributed or decentralized detection and estimation in applications such as wireless sensor networks has often been considered in the framework of parametric models, in which strong assumptions are made about a statistical description of nature. In certain applications, such assumptions are warranted and systems designed from these models show promise. However, in other scenarios, prior knowledge is at best vague and translating such knowledge into a statistical model is undesirable. Applications such as these pave the way for a nonparametric study of distributed detection and estimation. In this paper, we review recent work of the authors in which some elementary models for distributed learning are considered. These models are in the spirit of classical work in nonparametric statistics and are applicable to wireless sensor networks.

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Optimized opportunistic multicast scheduling (OMS) is studied for cellular networks, where the problem of efficiently transmitting a common set of fountain-encoded data from a single base station to multiple users over quasi-static fading channels is examined. The proposed OMS scheme better balances the tradeoff between multiuser diversity and multicast gain by transmitting to a subset of users in each time slot using the maximal data rate that ensures successful decoding by these users. We first analyze the system delay in homogeneous networks by capitalizing on extreme value theory and derive the optimal selection ratio (i.e., the portion of users that are selected in each time slot) that minimizes the delay. Then, we extend results to heterogeneous networks where users are subject to different channel statistics. By partitioning users into multiple approximately homogeneous rings, we turn a heterogeneous network into a composite of smaller homogeneous networks and drive the optimal selection ratio for the heterogeneous network. Computer simulations confirm theoretical results and illustrate that the proposed OMS can achieve significant performance gains in both homogeneous and heterogeneous networks as compared with the conventional unicast and broadcast scheduling. IEEE Transactions on Wireless CommunicationsThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-Optimized opportunistic multicast scheduling (OMS) is studied for cellular networks, where the problem of efficiently transmitting a common set of fountain-encoded data from a single base station to multiple users over quasi-static fading channels is examined. The proposed OMS scheme better balances the tradeoff between multiuser diversity and multicast gain by transmitting to a subset of users in each time slot using the maximal data rate that ensures successful decoding by these users. We first analyze the system delay in homogeneous networks by capitalizing on extreme value theory and derive the optimal selection ratio (i.e., the portion of users that are selected in each time slot) that minimizes the delay. Then, we extend results to heterogeneous networks where users are subject to different channel statistics. By partitioning users into multiple approximately homogeneous rings, we turn a heterogeneous network into a composite of smaller homogeneous networks and derive the optimal selection ratio for the heterogen...

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