On the Geometry of Censored Models

Abstract

This paper looks at the process of censoring via the differential geometric theory of Amari (1990) . This theory gives both a conceptual framework and a set of useful tools which help in mastering the asymptotic theory of estimation and testing. After briefly reviewing results from the theory, noting the natural geometry enjoyed by exponential and curved exponential families, the paper examines how censoring can be viewed in a geometric way. In particular the issue of information loss and the sampling properties of estimators are examined. Throughout a visual approach is taken in order to aid intuition and to give insight into the geometric theory

Computational Information Geometry in Statistics: Foundations

“…It is assumed the random variable Z has an exponential distribution, but only Y = min{Z, t} is observed. As discussed in [17], this gives a one-dimensional curved exponential family inside a two dimensional regular exponential family. Figure 1 shows some of the details of the geometry of the curved exponential family which is created after censoring.…”

Computational information geometry: theory and practice

“…It is assumed the random variable Z has an exponential distribution but only Y = min{Z, t} is observed. As discussed in [28] this gives a one-dimensional curved exponential family inside a two dimensional regular exponential family of the form…”

Computational Information Geometry in Statistics: Theory and Practice

“…It was observed that a censored exponential distribution gives a reasonable, but not exact, fit. As discussed in [11], this gives a one-dimensional curved exponential family inside a two-dimensional regular exponential family of the form:…”