Random Weighting Approximation of M-estimators with Increasing Dimensions of Parameter

The random weighting (RW) approach, recognized as a flexible alternative to the classical bootstrap method, has been widely employed for approximating the distribution of parameter estimates.Nevertheless, existing theoretical results for the RW approach primarily address scenarios where the parameter dimension remains fixed.In this paper, we investigate the RW method of M-estimators under general parametric models with increasing dimensions.We establish that the RW estimator has the same asymptotic distribution as that of the parameter M-estimate, which suggests that statistical inference regarding the parameter M-estimate can proceed without estimating nuisance parameters involved in its asymptotic distribution.Statistical properties of the RW estimator, such as the Bahadur representation and convergence rate, are also established.Furthermore,