Statistical Inference of Partially Linear Spatial Autoregressive Model Under Constraint Conditions

In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients.In this paper,the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions.By combining series approximation method,twostage least squares method and Lagrange multiplier method,the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties.Furthermore,the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions,and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses.Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples.Furthermore,a real example is provided to illustrate the application of the proposed estimation and testing methods.

Dual context prior and refined prediction for semantic segmentation

Recently,the focus of semantic segmentation research has shifted to the aggregation of context prior and refined boundary.A typical network adopts context aggregation modules to extract rich semantic features.It also utilizes top-down connection and skips connections for refining boundary details.But it still remains disadvantage,an obvious fact is that the problem of false segmentation occurs as the object has very different textures.The fusion of weak semantic and low-level features leads to context prior degradation.To tackle the issue,we propose a simple yet effective network,which integrates dual context prior and spatial propagation-dubbed DSPNet.It extends two mainstreams of current segmentation researches:(1)Designing a dual context prior module,which pays attention to context prior again with a shortcut connection.(2)The network can inherently learn semantic aware affinity values for each pixel and refine the segmentation.We will present detailed comparisons,which perform on PASCAL VOC 2012 and Cityscapes.The result demonstrates the validation of our approach.