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Department of Statistics

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https://hdl.handle.net/10217/100518
These digital collections include theses, dissertations, and datasets from the Department of Statistics. Due to departmental name changes, materials from the following historical department are also included here: Mathematics and Statistics.

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Browsing Department of Statistics by Subject "autoregression"

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    Estimation of structural breaks in nonstationary time series
    (Colorado State University. Libraries, 2008) Hancock, Stacey, author; Davis, Richard A., advisor; Iyer, Hari K., advisor
    Many time series exhibit structural breaks in a variety of ways, the most obvious being a mean level shift. In this case, the mean level of the process is constant over periods of time, jumping to different levels at times called change-points. These jumps may be due to outside influences such as changes in government policy or manufacturing regulations. Structural breaks may also be a result of changes in variability or changes in the spectrum of the process. The goal of this research is to estimate where these structural breaks occur and to provide a model for the data within each stationary segment. The program Auto-PARM (Automatic Piecewise AutoRegressive Modeling procedure), developed by Davis, Lee, and Rodriguez-Yam (2006), uses the minimum description length principle to estimate the number and locations of change-points in a time series by fitting autoregressive models to each segment. The research in this dissertation shows that when the true underlying model is segmented autoregressive, the estimates obtained by Auto-PARM are consistent. Under a more general time series model exhibiting structural breaks, Auto-PARM's estimates of the number and locations of change-points are again consistent, and the segmented autoregressive model provides a useful approximation to the true process. Weak consistency proofs are given, as well as simulation results when the true process is not autoregressive. An example of the application of Auto-PARM as well as a source of inspiration for this research is the analysis of National Park Service sound data. This data was collected by the National Park Service over four years in around twenty of the National Parks by setting recording devices in several sites throughout the parks. The goal of the project is to estimate the amount of manmade sound in the National Parks. Though the project is in its initial stages, Auto-PARM provides a promising method for analyzing sound data by breaking the sound waves into pseudo-stationary pieces. Once the sound data have been broken into pieces, a classification technique can be applied to determine the type of sound in each segment.
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    Regression of network data: dealing with dependence
    (Colorado State University. Libraries, 2019) Marrs, Frank W., author; Fosdick, Bailey K., advisor; Breidt, F. Jay, committee member; Zhou, Wen, committee member; Wilson, James B., committee member
    Network data, which consist of measured relations between pairs of actors, characterize some of the most pressing problems of our time, from environmental treaty legislation to human migration flows. A canonical problem in analyzing network data is to estimate the effects of exogenous covariates on a response that forms a network. Unlike typical regression scenarios, network data often naturally engender excess statistical dependence -- beyond that represented by covariates -- due to relations that share an actor. For analyzing bipartite network data observed over time, we propose a new model that accounts for excess network dependence directly, as this dependence is of scientific interest. In an example of international state interactions, we are able to infer the networks of influence among the states, such as which states' military actions are likely to incite other states' military actions. In the remainder of the dissertation, we focus on situations where inference on effects of exogenous covariates on the network is the primary goal of the analysis, and thus, the excess network dependence is a nuisance effect. In this setting, we leverage an exchangeability assumption to propose novel parsimonious estimators of regression coefficients for both binary and continuous network data, and new estimators for coefficient standard errors for continuous network data. The exchangeability assumption we rely upon is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression of network data. Although the estimators we propose are aligned with many network models in the literature, our estimators are derived from the assumption of exchangeability rather than proposing a particular parametric model for representing excess network dependence in the data.