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Doctoral thesis (Dissertations and theses)
From censored to cross-sectional data: non and semiparametric new developments
Laurent, Géraldine
2014
 

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Abstract :
[en] In many statistical studies, an observation is evident: the available data are regularly right-censored. A censorship arises when, for different reasons, the data time of interest can not be observed. A data is so right-censored if, instead of observing its time of interest, a lower bound of this time is considered for this data. For example, the study duration can be shorter than the time of interest leading then to a correspondence between the observed times and the study end time. Moreover, these data can be obtained from cross-sectional process. Cross-sectional process selects only data in progress at a fixed time to constitute the studied sample, determining the data followed for the study. Therefore, cross-sectional process introduces left truncation. A data is described as left-truncated if its time of interest is larger or equal to a fixed time. It is in this context this thesis has been elaborated. The considered estimation problems for such data will be studied with a nonparametric or semiparametric approach. An approach is nonparametric or semiparametric if none assumption is supposed about the belonging to parametric family for the time of interest distribution function, solely based on qualitative hypotheses. These estimation methods have thus the advantage to be based on weaker assumptions in comparison with the parametric approaches. The aim of the different researches developed in this thesis is to improve the current estimation techniques. This thesis is organised in four parts. The first part (first chapter) determines the context of our researches through practical examples and a significant but not exhaustive literature overview as well as our motivation about the different researches presented in this thesis. To conclude this first part, our contributions in these researches are briefly explained. The second part (second chapter) presents a new estimation procedure for the parameters of the parametric conditional variance in the heteroscedastic regression situation applied to right-censored data. This procedure constructs artificial data to replace censored data exploiting a heteroscedastic regression model and then defines the optimal parameters from the least squares method. The interest of this research is to fill a gap in the current literature. The third part (third and fourth chapters) studies, in a regression context, the cross-sectional data, i.e. left-truncated and right-censored data, where the conditional truncation distribution function is supposed to be known. The innovation of the method proposed here consists in the use of information contained in the conditional truncation distribution function for the nonparametric estimation methods. Finally, the fourth part (fifth chapter) is devoted to the cross-sectional data examination but this time for nonparametric estimation of the time of interest distribution function. In this chapter, the truncation distribution function is supposed to belong to a parametric family and not known anymore. The relevance of this approach is due to this weaker assumption than one in the above part. This information about the truncation distribution function is also introduced in the nonparametric estimation. This thesis concludes with a set of suggestions related to possible future researches in these statistical fields.
Research center :
Centre for Quantitative Methods and Operations Management (QuantOM)
Disciplines :
Mathematics
Author, co-author :
Laurent, Géraldine ;  Université de Liège - ULiège > HEC-Ecole de gestion : UER > UER Opérations
Language :
English
Title :
From censored to cross-sectional data: non and semiparametric new developments
Defense date :
2014
Institution :
ULiège - Université de Liège
Degree :
doctorat en Sciences orientation Sciences Mathématiques
Promotor :
Heuchenne, Cédric ;  Université de Liège - ULiège > HEC Recherche > HEC Recherche: Business Analytics & Supply Chain Management
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since 05 June 2014

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