Summary
We investigate a class of statistical problems, where usual bootstrap methods fail, and discuss two alternative solutions. In particular, a stochastic procedure for constructing confidence sets is proposed. Special applications are the eigenvalues of a covariance matrix and minimum distance functionals.
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Beran, R., Millar, P.W.: Stochastic estimation and testing. Ann. Stat.15, 1131–1154 (1987)
Beran, R., Srivastava, M.S.: Bootstrap tests and confidence regions for functions of a covariance matrix. Ann. Stat.13, 95–115 (1985) Correction: Ann. Stat.15, 470–471 (1987)
Bretagnolle, J.: Lois limites du bootstrap de certaines fonctionelles. Ann. Inst. Henri Poincaré19, 281–296 (1983)
Eaton, M.L., Tyler, D.E.: On Wielandt's inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix. Ann. Stat.19, 260–271 (1991)
Gill, R.D.: Non and semi-parametric maximum likelihood estimators and the von Mises method. Scand. J. Stat.16, 97–128 (1989)
Hoffmann-Jørgensen, J.: Stochastic processes on Polish spaces. (unpublished, 1984)
Pollard, D.: The minimum distance method of testing. Metrika27, 43–70 (1980)
Reeds, J.A.: On the definition of von Mises functionals. Ph.D. dissertation, Harvard University, 1976
Vaart, A.W. van der, Wellner, J.A.: Prohorov and continuous mapping theorems in the Hoffmann-Jørgensen weak convergence theory, with applications to convolution and asymptotic minimax theorems. Preprint, 1989 Lecture Notes-Monograph Series, IMS, Hayward
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Work supported by the Miller Institute for Basic Research in Science, Berkeley