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Some Bootstrap Methods for Regression and Time Series


In the first part of the dissertation, we discuss a residual bootstrap method for high-dimensional ridge regression. If the dimension and sample size are of the same order asymptotically, and the singular values of the design matrix follow a power law decay, we show that the method is able to consistently approximate the distribution of certain linear contrasts of the estimated regression coefficients. An automatic procedure for selecting tuning parameters is proposed and is shown to perform well in numerical experiments.

In the last part of the dissertation, we propose a moment-adjusted autoregressive sieve bootstrap procedure for univariate time series. The new bootstrap procedure is shown to be consistent for various statistics and models where the original autoregressive sieve fails. The method is demonstrated to be effective through simulations. Furthermore, the moment-adjusted autoregressive sieve bootstrap procedure shows improved power for the detection of non-linear time series compared to the original autoregressive sieve.

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