Should be somehow similar to network histogram with updated likelihood:
$$L(\kappa, z ; A, X)=\sum_{{(a, b) \in k \times[k]}} \sum_{{ (i, j) \in z^{-1}(a) \times z^{-1}(b), i < j }} l_{i j}\left(\kappa_{a b}, A, X\right)$$
where $l_{i j}\left(\kappa_{a b}, A, X\right)=\left(A_{i j}-\kappa_{a b}^{\mathrm{T}} X_{i j}\right)^2, X_{i j}=\left(1, x_i, x_j\right)^{\mathrm{T}}$ is the vector of regressors, and $\kappa=$ $\left(\kappa_{a b}\right)_{(a, b) \in[k] \times[k]} \in \mathbb{R}^{3 \times k \times k}$ denotes the full set of $k^2$ local linear coefficient vectors. Thus, the least-squares estimator of $(\kappa, z)$ is
$$(\hat{\kappa}, \hat{z}) \in \underset{\kappa \in \mathbb{R}^{3 \times k \times k}, z \in \mathcal{Z}_{n, h}}{\arg \min } L(\kappa, z ; A, X) .$$
Should be somehow similar to network histogram with updated likelihood:
where$l_{i j}\left(\kappa_{a b}, A, X\right)=\left(A_{i j}-\kappa_{a b}^{\mathrm{T}} X_{i j}\right)^2, X_{i j}=\left(1, x_i, x_j\right)^{\mathrm{T}}$ is the vector of regressors, and $\kappa=$ $\left(\kappa_{a b}\right)_{(a, b) \in[k] \times[k]} \in \mathbb{R}^{3 \times k \times k}$ denotes the full set of $k^2$ local linear coefficient vectors. Thus, the least-squares estimator of $(\kappa, z)$ is