Similarity-based model for ordered categorical data
提出一种针对有序分类变量的新模型，证明其混合性和平稳性，推导自相关函数，证明最大似然估计的一致性和渐近正态性，并通过Netflix数据集验证。
In a large variety of applications, the data for a variable we wish to explain are ordered and categorical. In this paper, we present a new similarity-based model for the scenario and investigate its properties. We establish that the process is ψ-mixing and strictly stationary and derive the explicit form of the autocorrelation function in some special cases. Consistency and asymptotic normality of the maximum likelihood estimator of the model’s parameters are proven. A simulation study supports our findings. The results are applied to the Netflix data set, comprised of a survey on users’ grading of movies.