In this work, we propose a joint collaboration-compression framework for sequential estimation of a random vector parameter in a resource constrained wireless sensor network (WSN). Specifically, we propose a framework where the local sensors first collaborate (via a collaboration matrix) with each other. Then a subset of sensors selected to communicate with the FC linearly compress their observations before transmission. We design near-optimal collaboration and linear compression strategies under power constraints via alternating minimization of the sequential minimum mean square error. The objective function for collaboration design is generally non-convex. We establish correspondence between the sparse collaboration matrix and the non-sparse vector consisting of the nonzero elements of the collaboration matrix. Then, we reformulate and solve the collaboration design problem using quadratically constrained quadratic program (QCQP). The compression design problem is solved using the same methodology. We propose two versions of compression design, one centralized scheme where the compression strategies are derived at the FC and decentralized, where the local sensors compute their individual compression strategies independently. Importantly, we show that the proposed methods can also be used for estimating time-varying random vector parameters. Finally, numerical results are provided to demonstrate the effectiveness of the proposed framework.