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On the implementation of LIR: The case of simple linear regression with interval data

Cattaneo, Marco E.G.V.; Wiencierz, Andrea

Authors

Marco E.G.V. Cattaneo

Andrea Wiencierz



Abstract

This paper considers the problem of simple linear regression with interval-censored data. That is, n pairs of intervals are observed instead of the n pairs of precise values for the two variables (dependent and independent). Each of these intervals is closed but possibly unbounded, and contains the corresponding (unobserved) value of the dependent or independent variable. The goal of the regression is to describe the relationship between (the precise values of) these two variables by means of a linear function. Likelihood-based Imprecise Regression (LIR) is a recently introduced, very general approach to regression for imprecisely observed quantities. The result of a LIR analysis is in general set-valued: it consists of all regression functions that cannot be excluded on the basis of likelihood inference. These regression functions are said to be undominated. Since the interval data can be unbounded, a robust regression method is necessary. Hence, we consider the robust LIR method based on the minimization of the residuals’ quantiles. For this method, we prove that the set of all the intercept-slope pairs corresponding to the undominated regression functions is the union of finitely many polygons. We give an exact algorithm for determining this set (i.e., for determining the set-valued result of the robust LIR analysis), and show that it has worst-case time complexity O(n3logn) . We have implemented this exact algorithm as part of the R package linLIR.

Citation

Cattaneo, M. E., & Wiencierz, A. (2014). On the implementation of LIR: The case of simple linear regression with interval data. Computational statistics, 29(3-4), 743-767. https://doi.org/10.1007/s00180-013-0459-9

Journal Article Type Article
Acceptance Date Oct 9, 2013
Online Publication Date Nov 5, 2013
Publication Date 2014-06
Deposit Date Jun 29, 2018
Journal Computational Statistics
Print ISSN 0943-4062
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 29
Issue 3-4
Pages 743-767
DOI https://doi.org/10.1007/s00180-013-0459-9
Keywords Interval-censored data; Nonparametric likelihood inference; Robust regression; Least median of squares; Exact algorithm; R package
Public URL https://hull-repository.worktribe.com/output/901307
Publisher URL https://link.springer.com/article/10.1007%2Fs00180-013-0459-9
Contract Date Jun 29, 2018