INCONSISTENCY OF THE BOOTSTRAP
REFERENCES
405
Ž
.
ANDREWS, D. W. K. 1997 : ‘‘A Simple Counterexample to the Bootstrap,’’ unpublished manuscript,
Cowles Foundation for Research in Economics, Yale University.
Ž
.
ᎏᎏᎏ 1998 : ‘‘Estimation When a Parameter Is on a Boundary: Part II,’’ unpublished manuscript,
Cowles Foundation for Research in Economics, Yale University.
Ž
.
Ž
ᎏᎏᎏ 1999 : ‘‘Estimation When a Parameter Is on a Boundary,’’ Econometrica, 67, 1341᎐1383.
.
ARCONES, M. 1990 : ‘‘On the Asymptotic Theory of the Bootstrap,’’ Ph.D. dissertation, The City
University of New York.
ATHREYA, K. B. 1987 : ‘‘Bootstrap of the Mean in the Infinite Variance Case,’’ Annals of Statistics,
15, 724᎐731.
Ž
.
Ž
.
ATHREYA, K. B., AND J. FUKUCHI 1994 : ‘‘Bootstrapping Extremes of I.I.D. Random Variables,’’
Proceedings of the Conference on Extreme Value Theory, NIST.
Ž
.
BABU, J. 1984 : ‘‘Bootstrapping Statistics with Linear Combinations of Chi-squares as Weak Limit,’’
Sankhya, 46, 86᎐93.
Ž
.
BASAWA, I. V., A. K. MALLIK, W. P. MCCORMICK, J. H. REEVES, AND R. L. TAYLOR 1991 :
‘‘Bootstrapping Unstable First-order Autoregressive Processes,’’ Annals of Statistics, 19,
1098᎐1101.
Ž
.
BERAN, R. 1982 : ‘‘Estimated Sampling Distributions: The Bootstrap and Competitors,’’ Annals of
Statistics, 10, 212᎐225.
Ž
.
ᎏᎏᎏ 1997 : ‘‘Diagnosing Bootstrap Success,’’ Annals of the Institute of Statistical Mathematics, 49,
1᎐24.
Ž
.
BERAN, R., AND M. S. SRIVASTAVA 1985 : ‘‘Bootstrap Tests and Confidence Regions for Functions
of a Covariance Matrix,’’ Annals of Statistics, 13, 95᎐115.
Ž
.
BICKEL, P. J., AND D. FREEDMAN 1981 : ‘‘Some Asymptotic Theory for the Bootstrap,’’ Annals of
Statistics, 9, 1196᎐1217.
Ž
.
BICKEL, P. J., F. GOTZE, AND W. R. VAN ZWET 1997 : ‘‘Resampling Fewer than n Observations:
¨
Gains, Losses, and Remedies for Losses,’’ Statistica Sinica, 7, 1᎐31.
BRETAGNOLLE, J. 1983 : ‘‘Lois Limites du Bootstrap de Certaines Fonctionnelles,’’ Annales de
L’institut Henri Poincare, Sec. B, 19, 281᎐296.
Ž
.
´
Ž
.
DATTA, S. 1995 : ‘‘On a Modified Bootstrap for Certain Asymptotically Non-normal Statistics,’’
Statistics and Probability Letters, 24, 91᎐98.
DEHEUVELS, P., D. MASON, AND G. SHORACK Ž1993 : ‘‘Some Results on the Influence of Extremes on
.
the Bootstrap,’’ Annales de l’Institut Henri Poincare, 29, 83᎐103.
´
Ž
.
DUMBGEN, L. 1993 : ‘‘On Nondifferentiable Functions and the Bootstrap,’’ Probability Theory and
¨
Related Fields, 95, 125᎐140.
Ž
.
EFRON, B. 1979 : ‘‘Bootstrap Methods: Another Look at the Jackknife,’’ Annals of Statistics, 7, 1᎐26.
EFRON, B., AND R. TIBSHIRANI 1993 : An Introduction to the Bootstrap. New York: Chapman and
Ž
.
Hall.
Ž
.
.
FREEDMAN, D. 1981 : ‘‘Bootstrapping Regression Models,’’ Annals of Statistics, 9, 1218᎐1228.
HALL, P. 1992 : The Bootstrap and Edgeworth Expansion. New York: Springer-Verlag.
HALL, P., AND J. L. HOROWITZ 1996 : ‘‘Bootstrap Critical Values for Tests Based on Generalized-
Ž
Ž
.
Method-of-Moment Estimators,’’ Econometrica, 64, 891᎐916.
POLITIS, D. N., AND J. P. ROMANO Ž
.
1994 : ‘‘Large Sample Confidence Regions Based on Subsamples
under Minimal Assumptions,’’ Annals of Statistics, 22, 2031᎐2050.
Ž
.
PUTTER, H., AND W. R. VAN ZWET 1996 : ‘‘Resampling: Consistency of Substitution Estimators,’’
Annals of Statistics, 24, 2297᎐2318.
Ž
.
ROMANO, J. 1988 : ‘‘Bootstrapping the Mode,’’ Annals of the Institute of Statistical Mathematics, 40,
565᎐586.
Ž
.
SRIRAM, T. N. 1993 : ‘‘Invalidity of the Bootstrap for Critical Branching Processes with Immigra-
tion,’’ Annals of Statistics, 22, 1013᎐1023.
Ž
.
Ž
.
SWANEPOEL, J. W. H. 1986 : ‘‘A Note on Proving That the Modified Bootstrap Works,’’ Communi-
cations in StatisticsᎏTheory and Methods Section, 15, 3193᎐3203.
Ž
.
WU, C. F. J. 1990 : ‘‘On the Asymptotic Properties of the Jackknife Histogram,’’ Annals of Statistics,
18, 1438᎐1452.