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Blockwise bootstrap wavelet in nonparametric regression model with weakly dependent processes

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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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Authors and Affiliations

  1. School of Mathematics and System Sciences, Shandong University, Jinan, 250100, China

    Lu Lin

  2. School of Science, Nantong University, Nantong, 226019, China

    Yunzheng Fan

  3. Department of Accountant, Hunan Finance and Economics College, Changsha, 410205, China

    Lin Tan

Authors
  1. Lu Lin
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  2. Yunzheng Fan
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  3. Lin Tan
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Correspondence to Lu Lin.

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Lin, L., Fan, Y. & Tan, L. Blockwise bootstrap wavelet in nonparametric regression model with weakly dependent processes. Metrika 67, 31–48 (2008). https://doi.org/10.1007/s00184-006-0120-5

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  • DOI: https://doi.org/10.1007/s00184-006-0120-5

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