Robust regression and outlier detection
Robust regression and outlier detection
On Computing the Least Quantile of Squares Estimate
SIAM Journal on Scientific Computing
Updating beliefs with incomplete observations
Artificial Intelligence
Algorithmic Learning in a Random World
Algorithmic Learning in a Random World
Centre and Range method for fitting a linear regression model to symbolic interval data
Computational Statistics & Data Analysis
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
A linear regression model for imprecise response
International Journal of Approximate Reasoning
A robust method for linear regression of symbolic interval data
Pattern Recognition Letters
Estimation of a flexible simple linear model for interval data based on set arithmetic
Computational Statistics & Data Analysis
Computing the least median of squares estimator in time O(nd)
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Hi-index | 0.00 |
We introduce a new approach to regression with imprecisely observed data, combining likelihood inference with ideas from imprecise probability theory, and thereby taking different kinds of uncertainty into account. The approach is very general: it provides a uniform theoretical framework for regression analysis with imprecise data, where all kinds of relationships between the variables of interest may be considered and all types of imprecisely observed data are allowed. Furthermore, we propose a regression method based on this approach, where no parametric distributional assumption is needed and likelihood-based interval estimates of quantiles of the residuals distribution are used to identify a set of plausible descriptions of the relationship of interest. Thus, the proposed regression method is very robust and yields a set-valued result, whose extent is determined by the amounts of both kinds of uncertainty involved in the regression problem with imprecise data: statistical uncertainty and indetermination. In addition, we apply our robust regression method to an interesting question in the social sciences by analyzing data from a social survey. As result we obtain a large set of plausible relationships, reflecting the high uncertainty inherent in the analyzed data set.