Interval Estimation: An Information-Theoretic Approach

The overall theme of this dissertation is to develop new methodology for interval estimation and apply it to analyze information observed as intervals over some ranges. It contributes to the estimation and inference of these types of data. The main question is how to identify the correct underlying structure of the model generating these interval data, and then how policy implications or forecasting can be made. These types of problems are very difficult to analyze regardless of the data size. A major problem is how to separate the noise from the signal in the observed interval information such that the correct model (or class of models) is identified. The results of this dissertation have theoretical as well as practical relevance and can be used to analyze emerging research frontiers of interval-valued data modeling. Chapter 2 develops an efficient information-theoretic estimator for analyzing interval-valued, and symbolic, data. Rather than applying the traditional least squares or likelihood methods to estimate some moments of the intervals (as often done), the proposed method uses the complete information in the sample and identifies the best model (parameters) that is consistent with the data generating process. It is an iterative approach. In addition, it imposes minimal structure and statistical assumptions. The chapter provides a large number of sampling experiments as well as a few empirical examples. Chapter 3 applies the iterative, information-theoretic estimator for analyzing and forecasting interval-valued data. The chapter concentrates on contrasting the proposed method's forecasts with competing approaches. It uses 13 years of SP 500 data to forecast up to five days ahead based on moving windows. The results show that for all periods the proposed approach has the lowest prediction errors: root mean squared errors and mean absolute errors for the lower and upper bounds. By using the full information contained in the interval of daily low and high returns, Chapter 3 finds that there are advantages in the estimation and prediction of a specific interval. In Chapter 4, the 2010 Kagera Health and Development Survey (KHDS 2010) from Tanzania is used to investigate whether gifts and transfers serve as insurance against health and income shocks and whether they have a systemic redistributive component: transfers flow from wealthy to poor, or vice-versa. It is well-know in the risk-sharing literature that there exist huge discrepancies between gifts and transfers self-reported by receiving and giving households. The common approach has been choosing only one of the self-reported values of receiver and giver or an average of the two. This chapter shows that depending on the transfers chosen, the result and inference may be different or incorrect. To address this issue, the transfers are modeled as interval and estimate the iterative IT method developed in Chapter 2. There is evidence that suggests risk-sharing against health and income shocks and no differential treatment between transitory, permanent, and persistent health shocks. In addition, there are suggestive findings of altruistic or social norms, helping among family networks of households. Geographical distance and social proximity measures such as kinship and sharing the same religion does play a role in determining gifts and transfers within family networks. By incorporating intervals of all observed or reported information, Chapter 4 can addressed a well-known issue of discordant information in ``dyadic" data.