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Title:

An exact algorithm for Likelihoodbased Imprecise Regression in the case

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of simple linear regression with interval data

of simple linear regression with interval data Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-17

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/smps12-uv.pdf

http://www.stat.uni-muenchen.de/~cattaneo/publications/smps12-uv.pdf Minimize

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text

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en

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Title:

Regression Analysis

Description:

ˆ Consider data on two

ˆ Consider data on two Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-25

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/slides-isipta11-2.pdf

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text

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en

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Title:

Helmut Küchenhoff

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Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between ...

Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-04-15

Source:

http://www.iser.essex.ac.uk/files/conferences/bhps/2009/abstracts/Christoph_Wunder.pdf

http://www.iser.essex.ac.uk/files/conferences/bhps/2009/abstracts/Christoph_Wunder.pdf Minimize

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text

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en

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001 Knowledge *(computed)*

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7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck, Austria, 2011 Regression with Imprecise Data: A Robust Approach

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We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominanc...

We introduce a robust regression method for imprecise data, and apply it to social survey data. Our method combines nonparametric likelihood inference with imprecise probability, so that only very weak assumptions are needed and different kinds of uncertainty can be taken into account. The proposed regression method is based on interval dominance: interval estimates of quantiles of the error distribution are used to identify plausible descriptions of the relationship of interest. In the application to social survey data, the resulting set of plausible descriptions is relatively large, reflecting the amount of uncertainty inherent in the analyzed data set. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-05-25

Source:

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-2.pdf

http://www.stat.uni-muenchen.de/%7Ecattaneo/publications/isipta11-2.pdf Minimize

Document Type:

text

Language:

en

Subjects:

imprecise data

imprecise data Minimize

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Title:

Likelihood-based Imprecise Regression

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We introduce a new approach to regression with imprecisely observed data, combining likelihood inference with ideas from imprecise probability theory, and thereby taking different kinds of uncertainty into account. The approach is very general: it provides a uniform theoretical framework for regression analysis with imprecise data, where all kin...

We introduce a new approach to regression with imprecisely observed data, combining likelihood inference with ideas from imprecise probability theory, and thereby taking different kinds of uncertainty into account. The approach is very general: it provides a uniform theoretical framework for regression analysis with imprecise data, where all kinds of relationships between the variables of interest may be considered and all types of imprecisely observed data are allowed. Furthermore, we propose a regression method based on this approach, where no parametric distributional assumption is needed and likelihood-based interval estimates of quantiles of the residuals distribution are used to identify a set of plausible descriptions of the relationship of interest. Thus, the proposed regression method is very robust and yields a set-valued result, whose extent is determined by the amounts of both kinds of uncertainty involved in the regression problem with imprecise data: statistical uncertainty and indetermination. In addition, we apply our robust regression method to an interesting question in the social sciences by analyzing data from a social survey. As result we obtain a large set of plausible relationships, reflecting the high uncertainty inherent in the analyzed data set. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-17

Source:

http://www.stat.uni-muenchen.de/~cattaneo/publications/ijar2-uv.pdf

http://www.stat.uni-muenchen.de/~cattaneo/publications/ijar2-uv.pdf Minimize

Document Type:

text

Language:

en

Subjects:

imprecise data ; likelihood inference ; imprecise probability ; complex uncertainty ; robust regression ; quantile

imprecise data ; likelihood inference ; imprecise probability ; complex uncertainty ; robust regression ; quantile Minimize

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310 Collections of general statistics *(computed)*

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Title:

Well-Being over the Life Span: Semiparametric Evidence from British and German Longitudinal Data

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This paper applies semiparametric regression models using penalized splines to investigate the profile of well-being over the life span. Splines have the advantage that they do not require a priori assumptions about the form of the curve. Using data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel Study (SOEP), ...

This paper applies semiparametric regression models using penalized splines to investigate the profile of well-being over the life span. Splines have the advantage that they do not require a priori assumptions about the form of the curve. Using data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel Study (SOEP), the analysis shows a common, quite similar, age-specific pattern of life satisfaction for both Britain and Germany that can be characterized by three age stages. In the first stage, life satisfaction declines until approximately the fifth life decade. In the second age stage, well-being clearly increases and has a second turning point (maximum) after which well-being decreases in the third age stage. Several reasons for the three-phase pattern are discussed. We point to the fact that neither polynomial functions of the third nor the fourth degree describe the relationship adequately: polynomials locate the minimum and the maximum imprecisely. In addition, our analysis discusses the indistinguishability of age, period, and cohort effects: we propose estimating age-period models that control for cohort effects including substantive variables, such as the life expectancy of the birth cohort, and further observed socioeconomic characteristics in the regression. ; Subjective well-being, life satisfaction, semiparametric regression, penalized splines, age-period model, age-cohort model Minimize

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Well-Being over the Life Span: Semiparametric Evidence from British and German Longitudinal Data

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This paper applies semiparametric regression models using penalized splines to investigate the profile of well-being over the life span. Splines have the advantage that they do not require a priori assumptions about the form of the curve. Using data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel Study (SOEP), ...

This paper applies semiparametric regression models using penalized splines to investigate the profile of well-being over the life span. Splines have the advantage that they do not require a priori assumptions about the form of the curve. Using data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel Study (SOEP), the analysis shows a common, quite similar, age-specific pattern of life satisfaction for both Britain and Germany that can be characterized by three age stages. In the first stage, life satisfaction declines until approximately the fifth life decade. In the second age stage, well-being clearly increases and has a second turning point (maximum) after which well-being decreases in the third age stage. Several reasons for the three-phase pattern are discussed. We point to the fact that neither polynomial functions of the third nor the fourth degree describe the relationship adequately: polynomials locate the minimum and the maximum imprecisely. In addition, our analysis discusses the indistinguishability of age, period, and cohort effects: we propose estimating age-period models that control for cohort effects including substantive variables, such as the life expectancy of the birth cohort, and further observed socioeconomic characteristics in the regression. ; subjective well-being, life satisfaction, semiparametric regression, penalized splines, age-period model, age-cohort model Minimize

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Title:

Regression analysis with imprecise data

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Statistical methods usually require that the analyzed data are correct and precise observations of the variables of interest. In practice, however, often only incomplete or uncertain information about the quantities of interest is available. The question studied in the present thesis is, how a regression analysis can reasonably be performed when...

Statistical methods usually require that the analyzed data are correct and precise observations of the variables of interest. In practice, however, often only incomplete or uncertain information about the quantities of interest is available. The question studied in the present thesis is, how a regression analysis can reasonably be performed when the variables are only imprecisely observed. At first, different approaches to analyzing imprecisely observed variables that were proposed in the Statistics literature are discussed. Then, a new likelihood-based methodology for regression analysis with imprecise data called Likelihood-based Imprecise Regression is introduced. The corresponding methodological framework is very broad and permits accounting for coarsening errors, in contrast to most alternative approaches to analyzing imprecise data. The methodology suggests considering as the result of a regression analysis the entire set of all regression functions that cannot be excluded in the light of the data, which can be interpreted as a confidence set. In the subsequent chapter, a very general regression method is derived from the likelihood-based methodology. This regression method does not impose restrictive assumptions about the form of the imprecise observations, about the underlying probability distribution, and about the shape of the relationship between the variables. Moreover, an exact algorithm is developed for the special case of simple linear regression with interval data and selected statistical properties of this regression method are studied. The proposed regression method turns out to be robust in terms of a high breakdown point and to provide very reliable insights in the sense of a set-valued result with a high coverage probability. In addition, an alternative approach proposed in the literature based on Support Vector Regression is studied in detail and generalized by embedding it into the framework of the formerly introduced likelihood-based methodology. In the end, the discussed regression methods are applied to two practical questions. ; Methoden der statistischen Datenanalyse setzen in der Regel voraus, dass die vorhandenen Daten präzise und korrekte Beobachtungen der untersuchten Größen sind. Häufig können aber bei praktischen Studien die interessierenden Werte nur unvollständig oder unscharf beobachtet werden. Die vorliegende Arbeit beschäftigt sich mit der Fragestellung, wie Regressionsanalysen bei unscharfen Daten sinnvoll durchgeführt werden können. Zunächst werden verschiedene Ansätze zum Umgang mit unscharf beobachteten Variablen diskutiert, bevor eine neue Likelihood-basierte Methodologie für Regression mit unscharfen Daten eingeführt wird. Als Ergebnis der Regressionsanalyse wird bei diesem Ansatz keine einzelne Regressionsfunktion angestrebt, sondern die gesamte Menge aller anhand der Daten plausiblen Regressionsfunktionen betrachtet, welche als Konfidenzbereich für den untersuchten Zusammenhang interpretiert werden kann. Im darauffolgenden Kapitel wird im Rahmen dieser Methodologie eine Regressionsmethode entwickelt, die sehr allgemein bezüglich der Form der unscharfen Beobachtungen, der möglichen Verteilungen der Zufallsgrößen sowie der Form des funktionalen Zusammenhangs zwischen den untersuchten Variablen ist. Zudem werden ein exakter Algorithmus für den Spezialfall der linearen Einfachregression mit Intervalldaten entwickelt und einige statistische Eigenschaften der Methode näher untersucht. Dabei stellt sich heraus, dass die entwickelte Regressionsmethode sowohl robust im Sinne eines hohen Bruchpunktes ist, als auch sehr verlässliche Erkenntnisse hervorbringt, was sich in einer hohen Überdeckungswahrscheinlichkeit der Ergebnismenge äußert. Darüber hinaus wird in einem weiteren Kapitel ein in der Literatur vorgeschlagener Alternativansatz ausführlich diskutiert, der auf Support Vector Regression aufbaut. Dieser wird durch Einbettung in den methodologischen Rahmen des vorher eingeführten Likelihood-basierten Ansatzes weiter verallgemeinert. Abschließend werden die behandelten Regressionsmethoden auf zwei praktische Probleme angewandt. Minimize

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

2013-12-13

Document Type:

Dissertation ; NonPeerReviewed

Subjects:

Fakultät für Mathematik ; Informatik und Statistik

Fakultät für Mathematik ; Informatik und Statistik Minimize

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801 Philosophy & theory *(computed)*

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Title:

Well-being over the life span: semiparametric evidence from British and German longitudinal data

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This paper applies semiparametric regression models using penalized splines to investigate the profile of well-being over the life span. Splines have the advantage that they do not require a priori assumptions about the form of the curve. Using data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel Study (SOEP), ...

This paper applies semiparametric regression models using penalized splines to investigate the profile of well-being over the life span. Splines have the advantage that they do not require a priori assumptions about the form of the curve. Using data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel Study (SOEP), the analysis shows a common, quite similar, age-specific pattern of life satisfaction for both Britain and Germany that can be characterized by three age stages. In the first stage, life satisfaction declines until approximately the fifth life decade. In the second age stage, well-being clearly increases and has a second turning point (maximum) after which well-being decreases in the third age stage. Several reasons for the three-phase pattern are discussed. We point to the fact that neither polynomial functions of the third nor the fourth degree describe the relationship adequately: polynomials locate the minimum and the maximum imprecisely. In addition, our analysis discusses the indistinguishability of age, period, and cohort effects: we propose estimating age-period models that control for cohort effects including substantive variables, such as the life expectancy of the birth cohort, and further observed socioeconomic characteristics in the regression. Minimize

Publisher:

Deutsches Institut für Wirtschaftsforschung (DIW) Berlin

Year of Publication:

2009

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

C14 ; C23 ; D10 ; I31 ; ddc:330 ; Subjective well-being ; life satisfaction ; semiparametric regression ; penalized splines ; age-period model ; age-cohort model ; Lebenszufriedenheit ; Lebensverlauf ; Kohortenanalyse ; Deutschland ; Großbritannien

C14 ; C23 ; D10 ; I31 ; ddc:330 ; Subjective well-being ; life satisfaction ; semiparametric regression ; penalized splines ; age-period model ; age-cohort model ; Lebenszufriedenheit ; Lebensverlauf ; Kohortenanalyse ; Deutschland ; Großbritannien Minimize

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Discussion papers // German Institute for Economic Research 889

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Title:

Well-being over the life span: semiparametric evidence from British and German longitudinal data

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This paper applies semiparametric regression models using penalized splines to investigate the profile of well-being over the life span. Splines have the advantage that they do not require a priori assumptions about the form of the curve. Using data from the British Household Panel Survey (BHPS) and the German Socio-Economic Panel Study (SOEP), the analysis shows a common, quite similar, age-specific pattern of life satisfaction for both Britain and Germany that can be characterized by three age stages. In the first stage, life satisfaction declines until approximately the fifth life decade. In the second age stage, well-being clearly increases and has a second turning point (maximum) after which well-being decreases in the third age stage. Several reasons for the three-phase pattern are discussed. We point to the fact that neither polynomial functions of the third nor the fourth degree describe the relationship adequately: polynomials locate the minimum and the maximum imprecisely. In addition, our analysis discusses the indistinguishability of age, period, and cohort effects: we propose estimating age-period models that control for cohort effects including substantive variables, such as the life expectancy of the birth cohort, and further observed socioeconomic characteristics in the regression. Minimize

Publisher:

IZA Bonn

Year of Publication:

2009

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

C14 ; C23 ; D10 ; I31 ; ddc:330 ; Subjective well-being ; life satisfaction ; semiparametric regression ; penalized splines ; age-period model ; age-cohort model ; Lebenszufriedenheit ; Lebensverlauf ; Kohortenanalyse ; Deutschland ; Großbritannien

C14 ; C23 ; D10 ; I31 ; ddc:330 ; Subjective well-being ; life satisfaction ; semiparametric regression ; penalized splines ; age-period model ; age-cohort model ; Lebenszufriedenheit ; Lebensverlauf ; Kohortenanalyse ; Deutschland ; Großbritannien Minimize

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IZA discussion papers 4155

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