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In this paper, we address the problem of decentralized parameter estimation with a Wireless Sensor Network (WSN). The network is hierarchical in that sensors are grouped into clusters, being each cluster under the supervision of a cluster-head (CH). The CH is also in charge of consolidating the sensor observations into a local estimate before its transmission to the Fusion Center (FC). In this context, we ask ourselves about the impact of the packet collisions associated with contention-based multiple-access schemes on the overall distortion in the estimates. To that extent, we derive an approximate yet asymptotically tight expression of the distortion resulting from the adoption of the ALOHA protocol. On that basis, we find a closed-form expression of the optimal time split for sensor-to-CH and CH-to-FC communications. Throughout the paper, we adopt a TDMA reservation-based (i.e. collision-free) multiple-access scheme as a benchmark. Numerical and computer simulation results reveal that the approximations are accurate along with a number of interesting design trade-offs associated with contention- and reservation-based schemes. The analysis is carried out from a cross-layer perspective in that the distortion in the estimates is a function of a number of systems parameters from the PHY (e.g. quantization noise) and MAC (e.g. probability of packet collision) layers of the OSI stack.