Blockwise bootstrap wavelet in nonparametric regression model with weakly dependent processes |
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Authors: | Lu Lin Yunzheng Fan Lin Tan |
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Affiliation: | (1) School of Mathematics and System Sciences, Shandong University, Jinan, 250100, China;(2) School of Science, Nantong University, Nantong, 226019, China;(3) Department of Accountant, Hunan Finance and Economics College, Changsha, 410205, China |
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Abstract: | In this paper, we suggest a blockwise bootstrap wavelet to estimate the regression function in the nonparametric regression models with weakly dependent processes for both designs of fixed and random. We obtain the asymptotic orders of the biases and variances of the estimators and establish the asymptotic normality for a modified version of the estimators. We also introduce a principle to select the length of data block. These results show that the blockwise bootstrap wavelet is valid for general weakly dependent processes such as α-mixing, φ-mixing and ρ-mixing random variables. |
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Keywords: | Nonparametric regression Bootstrap Blockwise Wavelet Weak dependence |
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