Self Consistent Estimator for Interval Valued Data

• Activity Number: 187 - Contributed Poster Presentations: Korean International Statistical Society
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Korean International Statistical Society
• Author(s): Hye Jeong Choi* and Johan Lim and Xinlei (Sherry) Wang and Minjung Kwak
• Companies: Seoul National University and Seoul National University and Southern Methodist University and Yeungnam University
• Keywords: Interval valued data; self consistent estimator; nonparametric distribution function estimation

Abstract

In this paper, we propose a self consistent estimator (SCE) for estimating the distribution of a single variable corresponding to a two-dimensional random interval. A univariate representation for (two dimensional) interval valued data is not unique by nature, in particular when the interval valued data is min-max (MM) type. The literatures focus on the estimation of marginal histogram distribution motivated by the analysis for measurement error (ME) type interval valued data. For the marginal histogram, the empirical histogram estimator and nonparmetric kernel estimator are proposed. In this work, we define a new univariate representation, named as a self consistent marginal, for the interval valued data, and propose a SCE to estimate it. We theoretically and numerically investigate the properties of the SCE under various assumptions. We further illustrate the advantages of the SCE over existing estimators with an empirical example.