Interval estimation: An information theoretic approach
提出一种基于信息论的区间数据推断方法，通过最大化离散化区间上的熵来估计联合分布和边际分布，并以洛杉矶和纽约的百年天气模式为例展示应用。
We develop here an alternative information theoretic method of inference of problems in which all of the observed information is in terms of intervals. We focus on the unconditional case in which the observed information is in terms the minimal and maximal values at each period. Given interval data, we infer the joint and marginal distributions of the interval variable and its range. Our inferential procedure is based on entropy maximization subject to multidimensional moment conditions and normalization in which the entropy is defined over discretized intervals. The discretization is based on theory or empirically observed quantities. The number of estimated parameters is independent of the discretization so the level of discretization does not change the fundamental level of complexity of our model. As an example, we apply our method to study the weather pattern for Los Angeles and New York City across the last century.