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Abstract
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute residuals. A useful representation of the last problem is given to examine properties of the objective function and estimate the number of its local minima. It is shown that the exact number of local minima is equal to ${p+\lfloor(n1)/2\rfloor\choose{p}}$, where $p$ is the dimension of the regression model and $n$ is the number of observations. As applications of the results, three algorithms are also outlined.
Original language  English 

Title of host publication  Computational Statistics Vol. 1: COMPSTAT Proceedings of the 10th Symposium on Computational Statistics, Neuchatel, Switzerland, August 1992 
Editors  Y. Dodge, J. Whittaker 
Publisher  PhysicaVerlag 
Pages  471476 
ISBN (Electronic)  9783662268117 
ISBN (Print)  9783662268131 
DOIs  
State  Published  1992 
Scopus subject areas
 Statistics, Probability and Uncertainty
 Control and Optimization
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10th Symposium on Computational Statistics
Николай Кимович Кривулин (Participant)
24 Aug 1992 → 28 Aug 1992Activity: Attendance types › Participating in a conference, workshop, ...

An analysis of the least median of squares regression problem
Николай Кимович Кривулин (Speaker)
24 Aug 1992 → 28 Aug 1992Activity: Talk types › Oral presentation