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Asymptotics of SIMEX-based variance estimation

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Abstract

In this paper, we study the asymptotic properties of simulation extrapolation (SIMEX) based variance estimation that was proposed by Wang et al. (J R Stat Soc Series B 71:425–445, 2009). We first investigate the asymptotic normality of the parameter estimator in general parametric variance function and the local linear estimator for nonparametric variance function when permutation SIMEX (PSIMEX) is used. The asymptotic optimal bandwidth selection with respect to approximate mean integrated squared error (AMISE) for nonparametric estimator is also studied. We finally discuss constructing confidence intervals/bands of the parameter/function of interest. Other than applying the asymptotic results so that normal approximation can be used, we recommend a nonparametric Monte Carlo algorithm to avoid estimating the asymptotic variance of estimator. Simulation studies are carried out for illustration.

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, School of Finance and Statistics, East China Normal University, 200241, Shanghai, China

    Yun Fang

  2. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

    Li-Xing Zhu

  3. Yunnan University of Finance and Economics, Yunnan, China

    Li-Xing Zhu

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  1. Yun Fang
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  2. Li-Xing Zhu
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Correspondence to Li-Xing Zhu.

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Fang, Y., Zhu, LX. Asymptotics of SIMEX-based variance estimation. Metrika 75, 329–345 (2012). https://doi.org/10.1007/s00184-010-0329-1

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  • DOI: https://doi.org/10.1007/s00184-010-0329-1

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