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Biometrika 1992 79(1):113-130; doi:10.1093/biomet/79.1.113
© 1992 by Biometrika Trust
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Bootstrap likelihoods

A. C. DAVISON1, D. V. HINKLEY1 and B.J. WORTON2

1Department of Statistics, University of Oxford 1 South Parks Road, Oxford OX1 3TG, U.K.
2Department of Mathematics, University of Essex Wivenhoe Park, Colchester CO4 3SQ, U.K.

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.

Key Words: Curve fitting • Density estimation • Edgeworth expansion • Empirical likelihood • Exponential family • Importance sampling • Monte Carlo • Pivot • Quasi-likelihood • Regression • Saddlepoint approximation • Simulation


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