This paper concerns the use of simulation procedures to construct secondorder accurate con dence limits having coverage error of order O(n ). An explicit formula for the analytical adjustment required in Efron's (1987) BCa percentile method is derived, automatic percentile methods that do not require analytical adjustments are proposed, and variance-stabilizing transformations designed to impro...

on the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. the convergence of vn to the analytical solution is also proved. ...