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Hasse diagrams and the generalized PAV-algorithm for monotonic regression in several explanatory variables
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0003-1836-4200
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
2005 (English)In: Computational Statistics and Data Analysis, ISSN 0167-9473Article in journal (Refereed) Submitted
Abstract [en]

Monotonic regression is a nonparametric method for estimation ofmodels in which the expected value of a response variable y increases ordecreases in all coordinates of a vector of explanatory variables x = (x1, …, xp).Here, we examine statistical and computational aspects of our recentlyproposed generalization of the pool-adjacent-violators (PAV) algorithm fromone to several explanatory variables. In particular, we show how the goodnessof-fit and accuracy of obtained solutions can be enhanced by presortingobserved data with respect to their level in a Hasse diagram of the partial orderof the observed x-vectors, and we also demonstrate how these calculations canbe carried out to save computer memory and computational time. Monte Carlosimulations illustrate how rapidly the mean square difference between fittedand expected response values tends to zero, and how quickly the mean squareresidual approaches the true variance of the random error, as the number of observations increases up to 104.

Place, publisher, year, edition, pages
2005.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-13600OAI: oai:DiVA.org:liu-13600DiVA: diva2:21032
Available from: 2005-12-16 Created: 2005-12-16 Last updated: 2015-06-02
In thesis
1. Monotonic and Semiparametric Regression for the Detection of Trends in Environmental Quality Data
Open this publication in new window or tab >>Monotonic and Semiparametric Regression for the Detection of Trends in Environmental Quality Data
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2005. 53 p.
Series
Linköping Studies in Statistics, ISSN 1651-1700 ; 7Linköping Studies in Arts and Science, ISSN 0282-9800 ; 343
Keyword
Normalisation, Monotonic, Semiparametric, Temporal trends, fluctuations, global, local, Matematisk statistik, Icke-parametriska metoder
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-5124 (URN)91-85457-70-1 (ISBN)
Public defence
2005-12-16, BL32, B-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2005-12-16 Created: 2005-12-16 Last updated: 2014-09-05Bibliographically approved

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Burdakov, OlegGrimvall, AndersHussian, MohamedSysoev, Oleg

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