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- Burdakov, Oleg, 1953-, et al.
(författare)
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A generalised PAV algorithm for monotonic regression in several variables
- 2004
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Ingår i: COMPSTAT. Proceedings in Computational Statistics. - Heidelberg, NY : PhysicaVerlag/Springer. - 3790815543 ; , s. 761-767
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Konferensbidrag (refereegranskat)abstract
- We present a new algorithm for monotonic regression in one or more explanatory variables. Formally, our method generalises the well-known PAV (pool-adjacent-violators) algorithm from fully to partially ordered data. The computational complexity of our algorithm is O(n2). The goodness-of-fit to observed data is much closer to optimal than for simple averaging techniques.
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| 2. |
- Burdakov, Oleg, 1953-, et al.
(författare)
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An algorithm for isotonic regression problems
- 2004
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Ingår i: European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS. - Jyväskylä : University of Jyväskylä. - 9513918688 ; , s. 1-9
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Konferensbidrag (refereegranskat)abstract
- We consider the problem of minimizing the distance from a given n-dimensional vector to a set defined by constraintsof the form xi xj Such constraints induce a partial order of the components xi, which can be illustrated by an acyclic directed graph.This problem is known as the isotonic regression (IR) problem. It has important applications in statistics, operations research and signal processing. The most of the applied IR problems are characterized by a very large value of n. For such large-scale problems, it is of great practical importance to develop algorithms whose complexity does not rise with n too rapidly.The existing optimization-based algorithms and statistical IR algorithms have either too high computational complexity or too low accuracy of the approximation to the optimal solution they generate. We introduce a new IR algorithm, which can be viewed as a generalization of the Pool-Adjacent-Violator (PAV) algorithm from completely to partially ordered data. Our algorithm combines both low computational complexity O(n2) and high accuracy. This allows us to obtain sufficiently accurate solutions to the IR problems with thousands of observations.
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| 3. |
- Burdakov, Oleg, 1953-, et al.
(författare)
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An O(n2) algorithm for isotonic regression
- 2006
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Ingår i: Large-Scale Nonlinear Optimization. - New York : Springer Science+Business Media B.V.. - 0387300635 ; , s. 25-33
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We consider the problem of minimizing the distance from a given n-dimensional vector to a set defined by constraints of the form xi ≤ xj. Such constraints induce a partial order of the components xi, which can be illustrated by an acyclic directed graph. This problem is also known as the isotonic regression (IR) problem. IR has important applications in statistics, operations research and signal processing, with most of them characterized by a very large value of n. For such large-scale problems, it is of great practical importance to develop algorithms whose complexity does not rise with n too rapidly. The existing optimization-based algorithms and statistical IR algorithms have either too high computational complexity or too low accuracy of the approximation to the optimal solution they generate. We introduce a new IR algorithm, which can be viewed as a generalization of the Pool-Adjacent-Violator (PAV) algorithm from completely to partially ordered data. Our algorithm combines both low computational complexity O(n2) and high accuracy. This allows us to obtain sufficiently accurate solutions to IR problems with thousands of observations.
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| 6. |
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| 7. |
- Hussian, Mohamed, 1969-
(författare)
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Monotonic and Semiparametric Regression for the Detection of Trends in Environmental Quality Data
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Natural fluctuations in the state of the environment can long conceal or distort important trends in the human impact on our ecosystems. Accordingly, there is increasing interest in statistical normalisation techniques that can clarify the anthropogenic effects by removing meteorologically driven fluctuations and other natural variation in time series of environmental quality data. This thesis shows that semi- and nonparametric regression methods can provide effective tools for applying such normalisation to collected data. In particular, it is demonstrated how monotonic regression can be utilised in this context. A new numerical algorithm for this type of regression can accommodate two or more discrete or continuous explanatory variables, which enables simultaneous estimation of a monotonic temporal trend and correction for one or more covariates that have a monotonic relationship with the response variable under consideration. To illustrate the method, a case study of mercury levels in fish is presented, using body length and weight as covariates. Semiparametric regression techniques enable trend analyses in which a nonparametric representation of temporal trends is combined with parametrically modelled corrections for covariates. Here, it is described how such models can be employed to extract trends from data collected over several seasons, and this procedure is exemplified by discussing how temporal trends in the load of nutrients carried by the Elbe River can be detected while adjusting for water discharge and other factors. In addition, it is shown how semiparametric models can be used for joint normalisation of several time series of data.
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| 8. |
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| 9. |
- Hussian, Mohamed, 1969-, et al.
(författare)
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Monotonic regression for assessment of trends in environmental quality data
- 2004
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Ingår i: European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS. - Jyväskylä : University of Jyväskylä, Department of Mathematical Information Technology. - 9513918688 ; , s. 1-12
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Konferensbidrag (refereegranskat)abstract
- Monotonic regression is a non-parametric method that is designed especially for applications in which the expected value of a response variable increases or decreases in one or more explanatory variables. Here, we show how the recently developed generalised pool-adjacent-violators (GPAV) algorithm can greatly facilitate the assessment of trends in time series of environmental quality data. In particular, we present new methods for simultaneous extraction of a monotonic trend and seasonal components, and for normalisation of environmental quality data that are influenced by random variation in weather conditions or other forms of natural variability. The general aim of normalisation is to clarify the human impact on the environment by suppressing irrelevant variation in the collected data. Our method is designed for applications that satisfy the following conditions: (i) the response variable under consideration is a monotonic function of one or more covariates; (ii) the anthropogenic temporal trend is either increasing or decreasing; (iii) the seasonal variation over a year can be defined by one increasing and one decreasing function. Theoretical descriptions of our methodology are accompanied by examples of trend assessments of water quality data and normalisation of the mercury concentration in cod muscle in relation to the length of the analysed fish.
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