Confidence Intervals from Stochastic Approximation

We propose a nonparametric method of constructing confidence interval for a scalar parameter from stochastic approximation through the efficient Robbins–Monro procedure proposed by Joseph (2004). Unlike the bootstrap method where the number of resampling is fixed in advance, the proposed procedure iteratively searches the endpoints in an optimal way such that the convergence is fast and the coverage is obtained accurately. Simulation and real data application illustrate its superiority over the usual Robbins–Monro procedure and common bootstrap methods.