Bootstrap Likelihoods
Copyright policy )Bootstrap Likelihoods
Summary: 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 \textit{A. B. Owen's} [ibid. 75, No. 2, 237-249 (1988; Zbl 0641.62032)] empirical likelihood.
kernel smoothing, quasi-likelihood, empirical likelihood, pivot, saddlepoint approximations, Density estimation, Edgeworth expansion, importance sampling methods, density estimation, exponential family, estimating equations, Nonparametric statistical resampling methods, regression, nested bootstrap, curve-fitting, bootstrap simulations, likelihood function, Monte Carlo, saddlepoint approximation
kernel smoothing, quasi-likelihood, empirical likelihood, pivot, saddlepoint approximations, Density estimation, Edgeworth expansion, importance sampling methods, density estimation, exponential family, estimating equations, Nonparametric statistical resampling methods, regression, nested bootstrap, curve-fitting, bootstrap simulations, likelihood function, Monte Carlo, saddlepoint approximation
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