Various Statistical Inferences for High-dimensional Time Series: Bootstrap, Homogeneity Pursuit and Autocovariance Test
This thesis aims to study various statistical inferences for high-dimensional data, especially high-dimensional time series, including sieve bootstrap, homogeneity pursuit, and an equivalence test for spiked eigenvalues of autocovariance matrix. The primary techniques used in this thesis are novel dimension-reduction methods developed from factor models and principal component analysis (PCA). Chapter 2 proposes a novel sieve bootstrap method for high-dimensional time series and applies it to...[Show more]
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