BOOTSTRAP LIKELIHOODS

For a given statistic, nested bootstrap calculations in conjunction with kernel smoothing methods are used to calculate estimates of the density of the statistic for a range of parameter values. These density estimates are then used to generate values of an analogue of a likelihood function, a whole function being obtained by curve-fitting methods. The application of importance sampling methods to the bootstrap simulations is described. An alternative version of the basic method is defined for cases involving estimating equations, and saddlepoint approximations are applied in place of simulations. The methods are illustrated in two examples. Numerical and theoretical comparisons are made to Owen's (1988) empirical likelihood.