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Allowing Left Truncated and Censored Fertility Data in the Normal Waiting Model
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
1995 (English)Report (Other academic)
Abstract [en]

Models describing marital fertility are under consideration. In Arnqvist (Research Report 2, Mathematical Statistics, Umeå University), a normal approximation of the waiting model was introduced. In this report a modification of the normal approximation is suggested. This specification allows the data to be left truncated and censored, which gives the possibility to apply the normally approximated waiting model in datasets as from the United Nations World Fertility Services. The model is appropriate except for extremely high fertility intensities, when it gives rise to bias in the parameter estimations. In this case, therefore, a bootstrap method is suggested to estimate and correct the bias. This means that the normal approximated waiting model is a good competitor to the well known Poisson or Coale-Trussell model. It also uses an understandable fertility specification.

Place, publisher, year, edition, pages
Umeå: Institute of Mathematical Statistics, Umeå University , 1995. , 21 p.
Series
Research Report, ISSN 1400-2701 ; 5
Keyword [en]
Coale-Trussell model, Poisson model, Waiting model, Normal approximated waiting model
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-130733OAI: oai:DiVA.org:umu-130733DiVA: diva2:1069788
Available from: 2017-01-30 Created: 2017-01-30 Last updated: 2017-02-01Bibliographically approved
In thesis
1. Functional clustering methods and marital fertility modelling
Open this publication in new window or tab >>Functional clustering methods and marital fertility modelling
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population.

The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions.

A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent curves. BVKMA is used on the varved lake sediment, to infer on climate, defined as frequencies of different weather types, over longer time periods.

Furthermore, a functional model-based clustering method is proposed that clusters subjects for which both functional data and covariates are observed, allowing different covariance structures in the different clusters. The model extends a model-based functional clustering method proposed by James and Suger (2003). An EM algorithm is derived to estimate the parameters of the model.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2017. 24 p.
Keyword
censoring, Coale-Trussell model, EM-algorithm, functional data analysis, functional clustering, marital fertility, normal approximation, Poisson process, varved lake sediments, warping
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-130734 (URN)978-91-7601-669-5 (ISBN)
Public defence
2017-02-24, Hörsal 1, Lindellhallen, Umeå Universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2017-02-03 Created: 2017-02-01 Last updated: 2017-02-09Bibliographically approved

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