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Bounded Influence Approaches to Constrained Mixed Vector Autoregressive Models

Gamalo, Mark Amper (2006) Bounded Influence Approaches to Constrained Mixed Vector Autoregressive Models. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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The proliferation of many clinical studies obtaining multiple biophysical signals from several individuals repeatedly in time is increasingly recognized, a recognition generating growth in statistical models that analyze cross-sectional time series data. In general, these statistical models try to answer two questions: (i) intra-individual dynamics of the response and its relation to some covariates; and, (ii) how this dynamics can be aggregated consistently in a group. In response to the first question, we propose a covariate-adjusted constrained Vector Autoregressive model, a technique similar to the STARMAX model (Stoffer, JASA 81, 762-772), to describe serial dependence of observations. In this way, the number of parameters to be estimated is kept minimal while offering flexibility for the model to explore higher order dependence. In response to (ii), we use mixed effects analysis that accommodates modelling of heterogeneity among cross-sections arising from covariate effects that vary from one cross-section to another. Although estimation of the model can proceed using standard maximum likelihood techniques, we believed it is advantageous to use bounded influence procedures in the modelling (such as choosing constraints) and parameter estimation so that the effects of outliers can be controlled. In particular, we use M-estimation with a redescending bounding function because its influence function is always bounded. Furthermore, assuming consistency, this influence function is useful to obtain the limiting distribution of the estimates. However, this distribution may not necessarily yield accurate inference in the presence of contamination as the actual asymptotic distribution might have wider tails. This led us to investigate bootstrap approximation techniques. A sampling scheme based on IID innovations is modified to accommodate the cross-sectional structure of the data. Then the M-estimation is applied to each bootstrap sample naively to obtain the asymptotic distribution of the estimates.We apply these strategies to the extracted BOLD activation from several regions of the brain from a group of individuals to describe joint dynamic behavior between these locations. We used simulated data with both innovation and additive outliers to test whether the estimation procedure is accurate despite contamination.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Gamalo, Mark
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairStoffer, David Sstoffer@stat.pitt.eduSTOFFER
Committee MemberJennings, J.
Committee MemberMazumdar, Satimaz1@pitt.eduMAZ1
Committee MemberThompson, Wesleywesleyt@pitt.eduWESLEYT
Date: 28 September 2006
Date Type: Completion
Defense Date: 8 June 2006
Approval Date: 28 September 2006
Submission Date: 6 July 2006
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: bootstrap approximation; cross-sectional time series; robust estimation; space-time models; vector autoregressive models
Other ID:, etd-07062006-142237
Date Deposited: 10 Nov 2011 19:50
Last Modified: 15 Nov 2016 13:45


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