TY - GEN

T1 - Efficient Randomized Algorithms for the Repeated Median Line Estimator

AU - Matousek, Jirí

AU - Mount, David M.

AU - Netanyahu, Nathan S.

N1 - Place of conference:Austin, Texas, USA

PY - 1993

Y1 - 1993

N2 - The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Recently there has been a great deal of interest is robust estimators, because of their lack of sensitivity to outlying data points. The basic measure of the robustness of an estimator is its breakdown point, that is, the fraction (up to 50%) of outlying data points that can corrupt the estimator. One problem with robust estimators is that achieving high breakdown points (near 50%) has proved to be computationally demanding. In this paper we present the best known theoretical algorithm and a practical subquadratic algorithm for computing a 50% breakdown point line estimator, the Siegel or repeated median line estimator. We first present an O(n log n) randomized expected time algorithm, where n is the number of given points. This algorithm relies, however, on sophisticated data structures. We also present a very simple O(n log 2 n) randomized algorit...

AB - The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Recently there has been a great deal of interest is robust estimators, because of their lack of sensitivity to outlying data points. The basic measure of the robustness of an estimator is its breakdown point, that is, the fraction (up to 50%) of outlying data points that can corrupt the estimator. One problem with robust estimators is that achieving high breakdown points (near 50%) has proved to be computationally demanding. In this paper we present the best known theoretical algorithm and a practical subquadratic algorithm for computing a 50% breakdown point line estimator, the Siegel or repeated median line estimator. We first present an O(n log n) randomized expected time algorithm, where n is the number of given points. This algorithm relies, however, on sophisticated data structures. We also present a very simple O(n log 2 n) randomized algorit...

UR - https://scholar.google.co.il/scholar?q=Efficient+Randomized+Algorithms+for+the+Repeated+Median+Line+Estimator&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

ER -