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Monotonic and Semiparametric Regression for the Detection of Trends in Environmental Quality Data
Linköping University, Department of Computer and Information Science, Statistics. Linköping University, Faculty of Arts and Sciences.
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 [en]
Normalisation, Monotonic, Semiparametric, Temporal trends, fluctuations, global, local
Keyword [sv]
Matematisk statistik, Icke-parametriska metoder
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-5124ISBN: 91-85457-70-1 (print)OAI: oai:DiVA.org:liu-5124DiVA: diva2:21036
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
List of papers
1. Hasse diagrams and the generalized PAV-algorithm for monotonic regression in several explanatory variables
Open this publication in new window or tab >>Hasse diagrams and the generalized PAV-algorithm for monotonic regression in several explanatory variables
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.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-13600 (URN)
Available from: 2005-12-16 Created: 2005-12-16 Last updated: 2015-06-02
2. Monotonic regression for the detection of temporal trends in environmental quality data
Open this publication in new window or tab >>Monotonic regression for the detection of temporal trends in environmental quality data
2005 (English)In: Match, ISSN 0340-6253, Vol. 54, no 3, 535-550 p.Article in journal (Refereed) Published
National Category
Social Sciences
Identifiers
urn:nbn:se:liu:diva-13601 (URN)
Available from: 2005-12-16 Created: 2005-12-16 Last updated: 2015-06-02
3. Trend analysis of mercury in fish using nonparametric regression
Open this publication in new window or tab >>Trend analysis of mercury in fish using nonparametric regression
2005 (English)Report (Other (popular science, discussion, etc.))
Abstract [en]

The International Council for the Exploration of the Sea (ICES) has longcompiled extensive data on contaminants in biota. We investigated how trendassessment of mercury in muscle tissue from fish (flounder and Atlantic cod)might be facilitated by using nonparametric regression to normalise observedlevels of this contaminant with respect to body length and weight. Specifically,we examined response surfaces and annual normalised means obtained byemploying purely additive models (AM), thin plate splines (TPS), andmonotonic regression (MR) to model mercury levels as functions of samplingyear and one or two covariates. Our analysis showed that TPS and MR modelscan be more satisfactory than purely additive models, because the formertechniques enable estimation of time-dependent relationships between themercury concentration and the covariates. However, the major obstacle fortrend assessment of the collected mercury data was a substantial interannualvariation that was related to factors other than body length and weight.Nevertheless, several time series of flounder data that started in the 1970s and1980s showed obvious downward trends, and these trends were particularly2strong in the Elbe estuary. When the analysis was limited to data collected after1990, an overall Mann-Kendall test for all sampling sites revealed astatistically significant downward trend for flounder, whereas it was notsignificant for cod.

Series
LIU-MAI-R, Department of Mathematics, Division of Statistics , 2005-07
Keyword
additive models, thin plate splines, monotonic regression, trend assessment, normalisation, mercury, fish
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-13602 (URN)
Available from: 2005-12-16 Created: 2005-12-16 Last updated: 2009-03-03
4. Estimation of the human impact on nutrient loads carried by the Elbe River
Open this publication in new window or tab >>Estimation of the human impact on nutrient loads carried by the Elbe River
2004 (English)In: Environmental Monitoring and Assessment, ISSN 0167-6369, Vol. 96, no 1-3, 15-33 p.Article in journal (Refereed) Published
Abstract [en]

The reunification of Germany led to dramatically reduced emissions of nitrogen (N) and phosphorus (P) to the environment. The aim of the present study was to examine how these exceptional decreases influenced the amounts of nutrients carried by the Elbe River to the North Sea. In particular, we attempted to extract anthropogenic signals from time series of riverine loads of nitrogen and phosphorus by developing a normalization technique that enabled removal of natural fluctuations caused by several weather-dependent variables. This analysis revealed several notable downward trends. The normalized loads of total-N and NO3-N exhibited an almost linear trend, even though the nitrogen surplus in agriculture dropped dramatically in 1990 and then slowly increased. Furthermore, the decrease in total-P loads was found to be considerably smaller close to the mouth of the river than further upstream. Studying the predictive ability of different normalization models showed the following: (i) nutrient loads were influenced primarily by water discharge; (ii) models taking into account water temperature, load of suspended particulate matter, and salinity were superior for some combinations of sampling sites and nutrient species; semiparametric normalization models were almost invariably better than ordinary regression models.

Keyword
Elbe River, nitrogen, normalization, phosphorus, trend detection
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-13603 (URN)10.1023/B:EMAS.0000031722.88972.62 (DOI)
Available from: 2005-12-16 Created: 2005-12-16 Last updated: 2009-05-19

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Hussian, Mohamed

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