<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>Consider a linear regression model where some or all of the observations of the dependent variable have been either rounded or interval-censored and only the resulting interval is available. Given a linear estimator β of the vector of regression parameters, we consider its possibilistic generalization for the model with rounded/censored data, which is called the OLS-set in the special case β = Ordinary Least Squares. We derive a geometric characterization of the set: we show that it is a zonotope in the parameter space. We show that even for models with a small number of regression parameters and a small number of observations, the combinatorial complexity of the polyhedron can be high. We therefore derive simple bounds on the OLS-set. These bounds allow to quantify the worst-case impact of rounding/censoring on the estimator β. This approach is illustrated by an example. We also observe that the method can be used for quantification of the rounding/censoring effect in advance, before the experiment is made, and hence can provide information on the choice of measurement precision when the experiment is being planned.</p></abstract>

Consider a linear regression model where some or all of the observations of the dependent variable have been either rounded or interval-censored and only the resulting interval is available. Given a linear estimator β of the vector of regression parameters, we consider its possibilistic generalization for the model with rounded/censored data, which is called the OLS-set in the special case β = Ordinary Least Squares. We derive a geometric characterization of the set: we show that it is a zonotope in the parameter space. We show that even for models with a small number of regression parameters and a small number of observations, the combinatorial complexity of the polyhedron can be high. We therefore derive simple bounds on the OLS-set. These bounds allow to quantify the worst-case impact of rounding/censoring on the estimator β. This approach is illustrated by an example. We also observe that the method can be used for quantification of the rounding/censoring effect in advance, before the experiment is made, and hence can provide information on the choice of measurement precision when the experiment is being planned.

On the Possibilistic Approach to Linear Regression with Rounded or Interval-Censored Data

Department of Econometrics, University of Economics, Winston Churchill Square 4, 130 67 Prague, Czech Republic

Measurement Science Review

Consider a linear regression model where some or all of the observations of the dependent variable have been either rounded or interval-censored and only the...

On the Possibilistic Approach to Linear Regression with Rounded or Interval-Censored Data

Published Online: Jun 03, 2011

Page range: 34 - 40

DOI: https://doi.org/10.2478/v10048-011-0007-0

Keywords
Linear regression, rounding, inexact data, interval-censored data

This content is open access.

On the Possibilistic Approach to Linear Regression with Rounded or Interval-Censored Data

Published Online: Jun 03, 2011

Page range: 34 - 40

DOI: https://doi.org/10.2478/v10048-011-0007-0

KeywordsLinear regression, rounding, inexact data, interval-censored data

This content is open access.

Keywords
Linear regression, rounding, inexact data, interval-censored data