Distributionally robust L<inf>1</inf>-estimation in multiple linear regression
MetadataShow full item record
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Linear regression is one of the most important and widely used techniques in data analysis, for which a key step is the estimation of the unknown parameters. However, it is often carried out under the assumption that the full information of the error distribution is available. This is clearly unrealistic in practice. In this paper, we propose a distributionally robust formulation of L1-estimation (or the least absolute value estimation) problem, where the only knowledge on the error distribution is that it belongs to a well-defined ambiguity set. We then reformulate the estimation problem as a computationally tractable conic optimization problem by using duality theory. Finally, a numerical example is solved as a conic optimization problem to demonstrate the effectiveness of the proposed approach.
Showing items related by title, author, creator and subject.
Chong, Yen N. (2001)General routing problems deal with transporting some commodities and/or travelling along the axes of a given network in some optimal manner. In the modern world such problems arise in several contexts such as distribution ...
Brcic, Ramon (2002)This thesis addresses some problems that arise in signal processing when the noise is impulsive and follows a heavy tailed distribution. After reviewing several of the more well known heavy- tailed distributions the common ...
Sithole, Moses M. (1997)This thesis is mainly concerned with the estimation of parameters in autoregressive models with censored data. For convenience, attention is restricted to the first-order stationary autoregressive (AR(1)) model in which ...