Numerical approximation of conditional asymptotic variances using Monte Carlo simulation (Q549619)

Let \(t_n\) be an asymptotically normal estimate for a parameter \(\vartheta\), i.e., \(\sqrt{n}(t_n-\vartheta)\to N(0,\nu_F)\) in law. The authors propose a new technique of numerical approximation for \(\nu_F\) based on the Richardson extrapolation of the variance of suitably truncated \(t_n\), say \(\tilde t_n\). The variances of \(\tilde t_n\) are estimated by simulated samples of two sizes \(n_1\) and \(n_2\), and then the approximation for \(\nu_F\) is derived from their asymptotic expansions up to the order \(O(n_i^{-3})\). A numerical example is presented for the estimation in a linear regression model with errors in variables.