We use a fast stepwise regression method, called orthogonal greedy algorithm (OGA) to select variables for high-dimensional time series model with measurement errors. Under a weak sparsity condition, we derive a convergence rate of OGA, which is expressed in terms of the number of iterations, the sample size and the order of the moment imposed on the error process. Under a strong sparsity condition, we develop a consistent model selection procedure using OGA and a high-dimensional information criterion.

中文摘要………………………………………………………………………… i
英文摘要…………………………………………………………………………. ii
1.Introduction………………………………………………………………….. 1
2.OGA and Noiseless OGA……………………………………………….. 3
3.Uniform Convergence Rate of Empirical Prediction Error……………………... 4
4.Sure Screening Property and Model Selection Consistency…………………….. 9
5.Simulation Studies……………………………………………….. 16
參考文獻…………………………………………………………………….…… 23
附錄………………………………………………………………………..………. .24

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