The behavior of a wireless sensor network dedicated to distributed estimation tasks may be significantly altered by the presence of nodes whose sensors are defective and produce erroneous measurements. This paper proposes and analyzes the performance of two distributed algorithms to help each node in determining whether it is equipped with a defective sensor. A node first collects data from its neighborhood, processes them to decide, using some generic local outlier detection test, whether these data contain outliers and broadcasts the result. Then, it determines the status of its own sensor using its result and those received from neighboring nodes. A single-decision and an iterative algorithm for defective sensor detection are proposed. Bounds on the performance of the single-decision algorithm are derived. A theoretical analysis of the probability of error and of the equilibrium of the iterative algorithm is provided for a wide class of local outlier detection tests. The trade-off between false alarm probability and detection probability is characterized theoretically and by simulation. MAC-layer issues, as well as the effect of packet losses are accounted for.