arXiv subjects

Joseph E. Yukich

Publications and source records attributed to Joseph E. Yukich.

3 recordsLinked to original sources

arXiv2019

Limit theory for unbiased and consistent estimators of statistics of random tessellations

We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling technique to construct an unbiased estimator of the average value of this geometric characteristic. Under mild conditions on the weights of the cells, we establish variance asymptotics and the asymptotic normality of the unbiased estimator as the observation window tends to the whole space. Moreover, the weak consistency is shown for this estimator.

math.PR↗

arXiv2016

Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances

We present a unified approach to goodness-of-fit testing in $\mathbb{R}^d$ and on lower-dimensional manifolds embedded in $\mathbb{R}^d$ based on sums of powers of weighted volumes of $k$-th nearest neighbor spheres. We prove asymptotic normality of a class of test statistics under the null hypothesis and under fixed alternatives. Under such alternatives, scaled versions of the test statistics converge to the $α$-entropy between probability distributions. A simulation study shows that the procedures are serious competitors to established goodness-of-fit tests.

stat.ME↗

arXiv2010

Energy Scaling Laws for Distributed Inference in Random Fusion Networks

The energy scaling laws of multihop data fusion networks for distributed inference are considered. The fusion network consists of randomly located sensors distributed i.i.d. according to a general spatial distribution in an expanding region. Among the class of data fusion schemes that enable optimal inference at the fusion center for Markov random field (MRF) hypotheses, the scheme with minimum average energy consumption is bounded below by average energy of fusion along the minimum spanning tree, and above by a suboptimal scheme, referred to as Data Fusion for Markov Random Fields (DFMRF). Scaling laws are derived for the optimal and suboptimal fusion policies. It is shown that the average asymptotic energy of the DFMRF scheme is finite for a class of MRF models.

cs.IT↗