Interval estimation: An information theoretic approach

ABSTRACT

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.

KEYWORDS:

• Discretization
• entropy
• information
• moment conditions
• weather patterns

JEL CLASSIFICATION:

• C13
• C51
• C63

Acknowledgment

The authors are thankful to Huancheng Du for his help with the empirical analysis and code, to Tuang Tual for his help constructing the figures, and to the participants of the conference in honor of Essie Maasoumi at Emory University for their helpful comments. We also thank the co-editor Peter Phillips and the three reviewers.