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In this paper, we study sparse signal detection problems in Degree Corrected Exponential Random Graph Models (ERGMs). We study the performance of two tests based on the conditionally centered sum of degrees and conditionally centered maximum of degrees, for a wide class of such ERGMs. The performance of these tests match the performance of the corresponding uncentered tests in the $beta$ model. Focusing on the degree corrected two star ERGM, we show that improved detection is possible at criticality using a test based on (unconditional) sum of degrees. In this setting we provide matching lower bounds in all parameter regimes, which is based on correlations estimates between degrees under the alternative, and of possible independent interest.
Environments with immobile obstacles or void regions that inhibit and alter the motion of individuals within that environment are ubiquitous. Correlation in the location of individuals within such environments arises as a combination of the mechanism
We prove the conjecture by Diaconis and Eriksson (2006) that the Markov degree of the Birkhoff model is three. In fact, we prove the conjecture in a generalization of the Birkhoff model, where each voter is asked to rank a fixed number, say r, of can
The $p_0$ model is an exponential random graph model for directed networks with the bi-degree sequence as the exclusively sufficient statistic. It captures the network feature of degree heterogeneity. The consistency and asymptotic normality of a dif
Structural changes occur in dynamic networks quite frequently and its detection is an important question in many situations such as fraud detection or cybersecurity. Real-life networks are often incompletely observed due to individual non-response or
Let $bY =bR+bX$ be an $Mtimes N$ matrix, where $bR$ is a rectangular diagonal matrix and $bX$ consists of $i.i.d.$ entries. This is a signal-plus-noise type model. Its signal matrix could be full rank, which is rarely studied in literature compared w