Inference for regression models with time series errors — Inverse autocovariance matrix estimation and high dimensional model selection

• Main Authors: Hai-Tang Chiou, 邱海唐
• Other Authors: Meihui Guo
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/3fv8sn

博士 === 國立中山大學 === 應用數學系研究所 === 105 === 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.