Title page for etd-0617117-113628


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URN etd-0617117-113628
Author Hai-Tang Chiou
Author's Email Address No Public.
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Department Applied Mathematics
Year 2016
Semester 2
Degree Ph.D.
Type of Document
Language English
Title Inference for regression models with time series errors — Inverse autocovariance matrix estimation and high dimensional model selection
Date of Defense 2017-07-03
Page Count 112
Keyword
  • modified Cholesky decomposition
  • long-memory processes
  • heteroscedasticity
  • location-dispersion model
  • orthogonal greedy algorithm
  • Abstract Linear regression is a well-known method to establish relationship between responses
    and explanatory variables, and has been used extensively in practical applications. This
    dissertation consists of two parts focus on statistical inference for linear regression models
    with time series errors. The first part concerns the problem of estimating inverse autocovariance
    matrices of long-memory processes admitting a linear representation. A modified
    Cholesky decomposition and an increasing order autoregressive model are adopted to construct
    the inverse autocovariance matrix estimate. We show that the proposed estimate is
    consistent in spectral norm. We further extend the result to linear regression models with
    long-memory time series errors. In particular, the same approach still works well based
    on the estimated least squares errors when our goal is to consistently estimate the inverse
    autocovariance matrix of the error process. Applications of this result to estimating
    unknown parameters in the aforementioned regression model are also given. Simulation
    studies are performed to confirm the theoretical results.
    In the second study of this dissertation, we consider model selection in sparse high-dimensional
    regression. High-dimensional model selection with independent and identically
    distributed errors is a much studied problem. However, little attention has been
    focused on heteroscedasticity and time series errors. This work aims at providing a consistent
    model selection procedure for high-dimensional sparse regression models with time
    series errors. We propose a high-dimensional sparse regression model with short- or long-
    range dependent errors. Moreover, our proposed model includes the location-dispersion
    model. The first step in our model selection procedure is to sequentially select predictors
    via an orthogonal greedy algorithm (OGA). To achieve consistent selection, we use a
    high-dimensional information criterion (HDIC) to remove irrelevant predictors. Simulation
    studies are conducted to illustrate our theoretical findings. In addition, we apply the
    approach to wafer acceptance test (WAT) data, and investigate and identify problematic tools.
    Advisory Committee
  • Mong-Na Lo Huang - chair
  • Shu-Hui Yu - co-chair
  • Henghsiu Tsai - co-chair
  • Hsin-Cheng Huang - co-chair
  • Shih-Feng Huang - co-chair
  • Meihui Guo - advisor
  • Ching-Kang Ing - advisor
  • Files
  • etd-0617117-113628.pdf
  • Indicate in-campus at 5 year and off-campus access at 5 year.
    Date of Submission 2017-07-17

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