In this work we propose a semiparametric bivariate copula whose density is defined by a piecewise constant function on disjoint squares. We obtain the maximum likelihood estimators of model parameters and prove that they reduce to the sample copula under specific conditions. We further propose to carry out a full Bayesian analysis of the model and introduce a spatial dependent prior distribution for the model parameters. This prior allows the parameters to borrow strength across neighbouring regions to produce smooth posterior estimates. To characterise the posterior distribution, via the full conditional distributions, we propose a data augmentation technique. A Metropolis-Hastings step is required and we propose a novel adaptation scheme for the random walk proposal distribution. We implement a simulation study and an analysis of a real dataset to illustrate the performance of our model and inference algorithms.

翻译：本文提出一种半参数二元连接函数，其密度由定义在不相交方块上的分段常数函数构成。我们给出了模型参数的极大似然估计量，并证明在特定条件下这些估计量退化为样本连接函数。进一步，我们提出对模型进行全贝叶斯分析，并为模型参数引入空间依赖先验分布。该先验允许参数借助邻近区域的信息进行强度借用，从而产生平滑的后验估计。为通过完全条件分布刻画后验分布，我们提出一种数据扩充技术。其中需采用Metropolis-Hastings步骤，并针对随机游走建议分布提出新的自适应方案。通过模拟实验和真实数据集分析，验证了模型及推断算法的性能。