i.e., [$$\begin{aligned}
            \sqrt{t+1}\left(\mathbf{x}_{n}(t)-\btheta\right)\overset{\mathcal{D}}{\Longrightarrow}\mathcal{N}\left(0,\left(N\mathbf{\Gamma}\right)^{-1}\right),
            \end{aligned}$$]{} where $\mathbf{\Gamma}=\frac{1}{N}\sum_{n=1}^{N}\mathbf{H}_{n}^{\top}\mathbf{R}_{n}^{-1}\mathbf{H}_{n}$ and $\overset{\mathcal{D}}{\Longrightarrow}$ denotes convergence in distribution. The above established asymptotic normality also points to the conclusion that the MSE decays as $\Theta(1/t)$. For future reference, we will refer to the distributed estimation approach in as the classical consensus+innovations approach. The aforementioned scheme, though optimal in terms of the asymptotic covariance entails the availability of global model information at each agent and exchange of the entire parameter estimate which in turn is $N$-dimensional among agents. Furthermore, due to the inherent spatial coupling in the observation sequence at each node with other nodes in its neighborhood, the availability of a particular entry of the state vector is localized to a small area. Hence, a large-scale deployment of such a system, would incorporate a significant delay for an agent to assimilate information about a particular entry of the state vector which is not local with respect to its neighborhood. Moreover, such a scheme requires the knowledge of the dimension of the state vector at each agent and storage of a high-dimensional local estimates, same as the size of the entire state vector. Such prior knowledge about attributes of the parameter such as dimension in conjunction with requirement 