This paper focuses on the problem of distributed composite
hypothesis testing in a network of sparsely interconnected
agents, in which only a small section of the field modeling
parametric alternatives is observable at each agent. A recursive
generalized likelihood ratio test (GLRT) type algorithm
in a distributed setup of the consensus-plus-innovations form
is proposed, in which the agents update their parameter estimates
and decision statistics by simultaneously processing
the latest sensed information (innovations) and information
obtained from neighboring agents (consensus). This paper
characterizes the conditions and the testing algorithm design
parameters which ensure that the probabilities of decision errors
decay to zero asymptotically in the large sample limit.
Finally, simulation studies are presented which illustrate the
findings.