Inference in semiparametric formation models for directed networks
We propose a semiparametric model for dyadic link formations in directed networks. The model contains a set of degree parameters that measure different effects of popularity or outgoingness across nodes, a regression parameter vector that reflects the homophily effect resulting from the nodal attrib...
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Zusammenfassung: | We propose a semiparametric model for dyadic link formations in directed
networks. The model contains a set of degree parameters that measure different
effects of popularity or outgoingness across nodes, a regression parameter
vector that reflects the homophily effect resulting from the nodal attributes
or pairwise covariates associated with edges, and a set of latent random noises
with unknown distributions. Our interest lies in inferring the unknown degree
parameters and homophily parameters. The dimension of the degree parameters
increases with the number of nodes. Under the high-dimensional regime, we
develop a kernel-based least squares approach to estimate the unknown
parameters. The major advantage of our estimator is that it does not encounter
the incidental parameter problem for the homophily parameters. We prove
consistency of all the resulting estimators of the degree parameters and
homophily parameters. We establish high-dimensional central limit theorems for
the proposed estimators and provide several applications of our general theory,
including testing the existence of degree heterogeneity, testing sparse signals
and recovering the support. Simulation studies and a real data application are
conducted to illustrate the finite sample performance of the proposed methods. |
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DOI: | 10.48550/arxiv.2405.19637 |