Three statistical problems involving model assessment of dependent data
Date
2024-12
Authors
Biswas, Eva
Major Professor
Advisor
Nordman, Daniel
Sabzikar, Farzad
Dutta, Somak
De Brabanter, Kris
Genschel, Ulrike
Committee Member
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Abstract
The dissertation considers three research problems that, while differing in nature and scope, are connected in a theme of model assessment for dependent data structures. The first problem involves establishing theory for smoothing filters that are used to estimate and diagnose the underlying trends in time series data from certain non-stationary long-range dependent processes. A focus is on the properties of the Hodrick-Prescott (HP) filter and a recently developed boosted version. The theory is illustrated in simulations and two real data examples that highlight the differences between simple HP filtering and the use of boosting. A second research problem proposes a formal goodness-of-fit test for diagnosing Markov random field models for spatial binary values having complicated dependence structures. Despite the prevalence and long history of such models for binary spatial data, appropriate model assessments have been lacking and this work directly addresses this difficult issue. The spatial model assessment is demonstrated in simulation and with applications to Besag's historical endive data as well as the breeding pattern of grasshopper sparrows across Iowa. A third research problem describes a new procedure for assessing rotational symmetry in data represented by three-dimensional rotation matrices. For such orientation data, symmetry is often assumed for simplifications in modeling, though there has been no formal way to diagnose whether such symmetry assumptions are appropriate for given data. A proposed test statistic based on empirical characteristic functions can formally assess symmetry properties, and a general bootstrap-based procedure for testing the rotational symmetry is developed. The performance of the bootstrap-based testing method is evaluated through numerical studies and applied to orientation data collected in texture analysis from materials science.
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Type
dissertation