gen.lms: Finding Likelihood-based Region Minimax (LRM) line(s)

Description

Function within the s.linlir-function that determines the Likelihood-based Region Minimax (LRM) line(s).

Usage

gen.lms(dat, p = 0.5, bet, epsilon = 0, k.u = 0)

Arguments

dat

An nx4 data.frame containing the imprecise data of the analyzed variables. Columns 1 and 2 correspond to the interval-valued observations of the regressor variable, columns 3 and 4 to those of the dependent variable.

Quantile of the abolute residuals' distribution to be used as loss function in the LIR analysis. (0.5 corresponds to the median.)

bet

Cutoff-point for the normalized profile likelihood function.

epsilon

Fraction of errors considered.

k.u

As default k.u is calculated on the basis of p, bet and epsilon.

Value

A list of two components.
lrmA vector (or a matrix) of the intercept and slope parameter values of the LRM line(s) and the value of the p-quantile of the absolute residuals associated with the LRM line(s).
max.bThe maximal absolute value of the considered slopes for the LRM line(s).

Details

The exact algorithm implemented by the function gem.lms can be seen as a generalization of the basic algorithm for Least Median of Squares Regression (see, e.g., Steele / Steiger (1986) and Rousseeuw / Leroy (1987)).

References

A. Wiencierz, M. Cattaneo (2012). An exact algorithm for Likelihood-based Imprecise Regression in the case of simple linear regression with interval data. (Accepted for the 6th International Conference on Soft Methods in Probability and Statistics (SMPS 2012). Publication in the series Advances in Intelligent and Soft Computing. Springer-Verlag.) M. Cattaneo, A. Wiencierz (2012). Likelihood-based Imprecise Regression. (Accepted for publication in the International Journal of Approximate Reasoning. A preliminary version of the paper is available as a research report at: http://epub.ub.uni-muenchen.de/12450/.) P. Rousseeuw, A. Leroy (1987). Robust Regression and Outlier Detection. Wiley J. Steele, W. Steiger (1986). Algorithms and complexity for least median of squares regression. Discret Appl Math 14. 93-100.