Functional Object Analysis: Toward Statistical Analysis of Functional Objects
Research output: Book/Report › Ph.D. thesis › Research
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Functional Object Analysis : Toward Statistical Analysis of Functional Objects . / Raket, Lars Lau.
Department of Computer Science, Faculty of Science, University of Copenhagen, 2014. 107 p.Research output: Book/Report › Ph.D. thesis › Research
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TY - BOOK
T1 - Functional Object Analysis
T2 - Toward Statistical Analysis of Functional Objects
AU - Raket, Lars Lau
PY - 2014
Y1 - 2014
N2 - We propose a direction it the field of statistics which we will call functional object analysis. This subfields considers the analysis of functional objects defined on continuous domains. In this setting we will focus on model-based statistics, with a particularly emphasis on mixed-effect formulations, where the observed functional signal is assumed to consist of both fixed and random functional effects. This thesis takes the initial steps toward the development of likelihood-based methodology for functional objects. We first consider analysis of functional data defined on high-dimensional Euclidean spaces under the effect of additive spatially correlated effects, and then move on to consider how to include data alignment in the statistical model as a nonlinear effect under additive correlated noise. In both cases, we will give directions on how to generalize the methodology to more complex data setups. Finally, we consider various extensions and future directions.
AB - We propose a direction it the field of statistics which we will call functional object analysis. This subfields considers the analysis of functional objects defined on continuous domains. In this setting we will focus on model-based statistics, with a particularly emphasis on mixed-effect formulations, where the observed functional signal is assumed to consist of both fixed and random functional effects. This thesis takes the initial steps toward the development of likelihood-based methodology for functional objects. We first consider analysis of functional data defined on high-dimensional Euclidean spaces under the effect of additive spatially correlated effects, and then move on to consider how to include data alignment in the statistical model as a nonlinear effect under additive correlated noise. In both cases, we will give directions on how to generalize the methodology to more complex data setups. Finally, we consider various extensions and future directions.
UR - https://soeg.kb.dk/permalink/45KBDK_KGL/fbp0ps/alma99122493905005763
M3 - Ph.D. thesis
BT - Functional Object Analysis
PB - Department of Computer Science, Faculty of Science, University of Copenhagen
ER -
ID: 123353008