This paper considers a network of sensors without fusion center that may be difficult to set up in applications involving sensors embedded on autonomous drones or robots. In this context, this paper considers that the sensors must perform a given clustering task in a fully decentralized setup. Standard clustering algorithms usually need to know the number of clusters and are very sensitive to initialization, which makes them difficult to use in a fully decentralized setup. In this respect, this paper proposes a decentralized model-based clustering algorithm that overcomes these issues. The proposed algorithm is based on a novel theoretical framework that relies on hypothesis testing and robust M-estimation. More particularly, the problem of deciding whether two data belong to the same cluster can be optimally solved via Wald's hypothesis test on the mean of a Gaussian random vector. The p-value of this test makes it possible to define a new type of score function, particularly suitable for devising an M-estimation of the centroids. The resulting decentralized algorithm efficiently performs clustering without prior knowledge of the number of clusters. It also turns out to be less sensitive to initialization than the already existing clustering algorithms, which makes it appropriate for use in a network of sensors without fusion center.