1991
DOI: 10.1016/0167-9473(91)90071-9
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An algorithm for isotonic median regression

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Cited by 5 publications
(9 citation statements)
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“…The following list of references on this problem demonstrates the level of interest in this problem in the field of operations research and statistics: Ayer et al (1955), Brunk (1955), Robertson and Waltman (1968), Gebhardt (1970), Barlow et al (1972), Robertson andWright (1973, 1980), Ubhaya (1974aUbhaya ( , 1974bUbhaya ( , 1979Ubhaya ( , 1987, Casady and Cryer (1976), Goldstein and Kruskal (1976), Dykstra (1981), Lee (1983), Maxwell and Muchstadt (1983), Roundy (1986), Menendez and Salvador (1987), Robertson et al (1988), Chakravarti (1989), Best and Chakravarti (1990), Stromberg (1991), Best and Tan (1993), Tamir (1993), Eddy et al (1995), Pardalos et al (1995), Shi (1995), Best et al (2000), Liu and Ubhaya (1997), Schell and Singh (1997), and Pardalos and Xue (1999). It is well known that the isotone regression problem for p = 1 can be solved in O n log n time, and for p = 2 and p = , it can be solved in O n time (see, for example, Best and Chakravarti 1990, Pardalos et al 1995, and Liu and Ubhaya 1997.…”
Section: Introductionmentioning
confidence: 99%
“…The following list of references on this problem demonstrates the level of interest in this problem in the field of operations research and statistics: Ayer et al (1955), Brunk (1955), Robertson and Waltman (1968), Gebhardt (1970), Barlow et al (1972), Robertson andWright (1973, 1980), Ubhaya (1974aUbhaya ( , 1974bUbhaya ( , 1979Ubhaya ( , 1987, Casady and Cryer (1976), Goldstein and Kruskal (1976), Dykstra (1981), Lee (1983), Maxwell and Muchstadt (1983), Roundy (1986), Menendez and Salvador (1987), Robertson et al (1988), Chakravarti (1989), Best and Chakravarti (1990), Stromberg (1991), Best and Tan (1993), Tamir (1993), Eddy et al (1995), Pardalos et al (1995), Shi (1995), Best et al (2000), Liu and Ubhaya (1997), Schell and Singh (1997), and Pardalos and Xue (1999). It is well known that the isotone regression problem for p = 1 can be solved in O n log n time, and for p = 2 and p = , it can be solved in O n time (see, for example, Best and Chakravarti 1990, Pardalos et al 1995, and Liu and Ubhaya 1997.…”
Section: Introductionmentioning
confidence: 99%
“…Robertson and Waltman (1968) studied the L, monotonic problem but they associate H,, with its central median, thus they ignore any other solution. Menendez and Salvador (1987) developed an algorithm for obtaining all monotonic solutions and provided Fortran codes for this algorithm. Stromberg (1991) replaced (1) by a general convex distance function and filled some theoretical gaps of the Menendez and Salvador constructive algorithm.…”
Section: Discussionmentioning
confidence: 99%
“…It is quite straightforward to verify that the current iterate and multipliers together satisfy conditions (2), (3), (5), (8), and (9). We verify (7) by an easy inductive argument, beginning with each sink of G. At the first inductive stage we verify (7) for each sink of G by using (14). At the second inductive stage we consider all "second sinks" of G; i.e., we consider all vertices wich are sinks of the graph obtained from G by deleting all its sinks.…”
Section: Validation Of the Algorithm; A Linearmentioning
confidence: 99%
“…At the second inductive stage we consider all "second sinks" of G; i.e., we consider all vertices wich are sinks of the graph obtained from G by deleting all its sinks. We verify (7) for each such vertex by using (14) and the result proved in the first inductive stage. Proceedng in this manner, we verify (7) for all vertices in finitely many stages.…”
Section: Validation Of the Algorithm; A Linearmentioning
confidence: 99%
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