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Estimation in a model with incidental parameters
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
2002 (English)Report (Other academic)
Abstract [en]

We study the maximum likelihood method together with bootstrap analysis and other uncertainty measures in a situation with both structural and incidental parameters and a rather simple parametric setting. Our purpose is to study methods that can be generalised to and used in more complicated situations of similar nature.

Two different approaches to the incidental parameters are treated, one deterministic and one random. Both approaches are shown to give similar results. When analysing the asymptotic properties of the estimator of the structural parameter, the profile likelihood, the delta method and the bootstrap analysis seem to be equally good in the deterministic case. The bootstrap also works well with a random interpretation of the incidental parameters.

Place, publisher, year, edition, pages
2002. , 18 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 02
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-86858OAI: oai:DiVA.org:liu-86858DiVA: diva2:582890
Available from: 2013-01-07 Created: 2013-01-07 Last updated: 2013-01-07
In thesis
1. Computer based statistical treatment in models with incidental parameters: inspired by car crash data
Open this publication in new window or tab >>Computer based statistical treatment in models with incidental parameters: inspired by car crash data
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Bootstrap and Markov chain Monte Carlo methods have received much attention in recent years. We study computer intensive methods that can be used in complex situations where it is not possible to express the likelihood estimates or the posterior analytically. The work is inspired by a set of car crash data from real traffic.

We formulate and develop a model for car crash data that aims to estimate and compare the relative collision safety among different car models. This model works sufficiently well, although complications arise due to a growing vector of incidental parameters. The bootstrap is shown to be a useful tool for studying uncertainties of the estimates of the structural parameters. This model is further extended to include driver characteristics. In a Poisson model with similar, but simpler structure, estimates of the structural parameter in the presence of incidental parameters are studied. The profile likelihood, bootstrap and the delta method are compared for deterministic and random incidental parameters. The same asymptotic properties, up to first order, are seen for deterministic as well as random incidental parameters.

The search for suitable methods that work in complex model structures leads us to consider Markov chain Monte Carlo (MCMC) methods. In the area of MCMC, we consider particularly the question of how and when to claim convergence of the MCMC run in situations where it is only possible to analyse the output values of the run and also how to compare different MCMC modellings. In Metropolis-Hastings algorithm, different proposal functions lead to different realisations. We develop a new convergence diagnostic, based on the Kullback-Leibler distance, which is shown to be particularly useful when comparing different runs. Comparisons with established methods turn out favourably for the KL.

In both models, a Bayesian analysis is made where the posterior distribution is obtained by MCMC methods. The credible intervals are compared to the corresponding confidence intervals from the bootstrap analysis and are shown to give the same qualitative conclusions.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2003. 34 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 814
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-22219 (URN)1377 (Local ID)91-7373-625-2 (ISBN)1377 (Archive number)1377 (OAI)
Public defence
2003-05-09, Sal Visionen, Hus B, Linköpings Universitet, Linköping, 13:15 (Swedish)
Opponent
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-01-07

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Vadeby, Anna

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • Other style
More styles
Language
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  • en-US
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  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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