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Monotonic regression for large multivariate datasetsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
##### Abstract [en]

##### Abstract [sv]

##### Place, publisher, year, edition, pages

Linköping: Linköping University Electronic Press , 2010. , 75 p.
##### Series

Linköping Studies in Statistics, ISSN 1651-1700 ; 11Linköping Studies in Arts and Science, ISSN 0282-9800 ; 514
##### National Category

Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:liu:diva-65349ISBN: 978-91-7393-412-1 (print)OAI: oai:DiVA.org:liu-65349DiVA: diva2:395118
##### Public defence

2010-04-16, Glashuset, Building B, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
##### Opponent

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Available from: 2011-02-04 Created: 2011-02-04 Last updated: 2012-11-08Bibliographically approved
##### List of papers

Monoton regression för stora multivariata datamateriaI (Swedish)

Monotonic regression is a non-parametric statistical 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. Such applications can be found in business, physics, biology, medicine, signal processing, and other areas. Inasmuch as many of the collected datasets can contain a very large number of multivariate observations, there is a strong need for efficient numerical algorithms. Here, we present new methods that make it feasible to fit monotonic functions to more than one hundred thousand data points. By simulation, we show that our algorithms have high accuracy and represent considerable improvements with respect to computational time and memory requirements. In particular , we demonstrate how segmentation of a large-scale problem can greatly improve the performance of existing algorithms. Moreover, we show how the uncertainty of a monotonic regression model can be estimated. One of the procedures we developed can be employed to estimate the variance of the random error present in the observed response. Other procedures are based on resampling techniques and can provide confidence intervals for the expected response at given levels of a set of predictors.

Monoton regression är en icke-parametrisk statistisk metod som är utvecklad speciellt för tillämpningar i vilka det förväntade värdet aven responsvariabel ökar eller minskar med en eller flera förklaringsvariabler. Sådana tillämpningar finns inom företagsekonomi, fysik, biologi, medicin, signalbehandling och andra områden. Eftersom många insamlade datamaterial kan innehålla ett mycket stort antal multivariata observationer finns ett starkt behov av effektiva numeriska algoritmer. Här presenterar vi nya metoder som gör det möjligt att anpassa monotona funktioner till mer än 100000 datapunkter. Genom simulering visar vi. att våra algoritmer har hög noggrannhet och innebär betydande förbättringar med avseende på beräkningstid och krav på minnesutrymme. Speciellt visar vi hur segmentering av ett storskaligt problem starkt kan förbättra existerande algoritmer. Dessutom visar vi hur osäkerheten aven monoton regressions modell kan uppskattas. En av de metoder vi utvecklat kan användas för att uppskatta variansen för de slumpkomponenter som kan finnas i den observerade responsvariabeln. Andra metoder, baserade på s.k. återsampling, kan ge konfidensintervall för den förväntade responsen för givna värden på ett antal prediktorer.

1. An *O*(*n*^{2}) algorithm for isotonic regression problems$(function(){PrimeFaces.cw("OverlayPanel","overlay357983",{id:"formSmash:j_idt485:0:j_idt489",widgetVar:"overlay357983",target:"formSmash:j_idt485:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Data preordering in generalized PAV algorithm for monotonic regression$(function(){PrimeFaces.cw("OverlayPanel","overlay257126",{id:"formSmash:j_idt485:1:j_idt489",widgetVar:"overlay257126",target:"formSmash:j_idt485:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Generalized PAV algorithm with block refinement for partially ordered monotonic regression$(function(){PrimeFaces.cw("OverlayPanel","overlay283960",{id:"formSmash:j_idt485:2:j_idt489",widgetVar:"overlay283960",target:"formSmash:j_idt485:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. A segmentation-based algorithm for large-scale partially ordered monotonic regression$(function(){PrimeFaces.cw("OverlayPanel","overlay424299",{id:"formSmash:j_idt485:3:j_idt489",widgetVar:"overlay424299",target:"formSmash:j_idt485:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Bootstrap estimation of the variance of the error term in monotonic regression models$(function(){PrimeFaces.cw("OverlayPanel","overlay536280",{id:"formSmash:j_idt485:4:j_idt489",widgetVar:"overlay536280",target:"formSmash:j_idt485:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Bootstrap confidence intervals for large-scale multivariate monotonic regression problems$(function(){PrimeFaces.cw("OverlayPanel","overlay565741",{id:"formSmash:j_idt485:5:j_idt489",widgetVar:"overlay565741",target:"formSmash:j_idt485:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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