In 1946 Paul Halmos studied unbiased estimators of minimum variance, and planted the
seed from which the subject matter of the present monograph sprang. The author has …

Let G be a graph and let X n count copies of G in a random graph K (n, p). The random
variable\left (X_n-E\left (X_n\right)\right)/Var\left (X_n\right) is asymptotically normally …

The application of Stein's method of obtaining rates of convergence to the normal
distribution is illustrated in the context of random graph theory. Problems which exhibit a …

Many economic activities are embedded in networks: sets of agents and the (often) rivalrous
relationships connecting them to one another. Input sourcing by firms, interbank lending …

We study the problem of testing for structure in networks using relations between the
observed frequencies of small subgraphs. We consider the statistics\begin {align*} T_3 …

This paper deals with rates of convergence in the CLT for certain types of dependency. The
main idea is to combine a modification of a theorem of Stein, requiring a coupling …

Network method of moments (Ann. Statist. 39 (2011) 2280–2301) is an important tool for
nonparametric network inference. However, there has been little investigation on accurate …

We consider the random variable S_ n, v (f)= ∑ i_1<...< i_v\leqq nf (X_ i_1,..., X_ i_v, Y_ i_1
i_2,..., Y_ i_ v-1 i_v), where X ii= 1/n and Y ij 1≦ i< i≦ n are two independent sequences of …

We derive sufficient conditions for a probability measure on a finite product space (a spin
system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions …

In this paper, we prove a local limit theorem for the distribution of the number of triangles in
the Erdos‐Rényi random graph G (n, p), where is a fixed constant. Our proof is based on …