Asymptotics of SIMEX-based variance estimation

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.

Estimation of variances and covariances for high‐dimensional data: a selective review

“…To overcome this problem, Carroll and Wang and Wang et al proposed permutation SIMEX methods that lead to consistent estimates of θ and g . Other regression methods include Fan et al and Fang and Zhu …”