Target estimation for bias and mean square error reduction

Annals of Statistics

Volumn 27, Issue 3, 1999, Pages 1080-1104

  Cabrera, Javier ^a   Fernholz, Luisa Turrin ^b  

^a RUTGERS UNIVERSITY   (United States)

^b TEMPLE UNIVERSITY   (United States)

Author keywords

Bias; Mean square error; Parametric family; Statistical functionals; Target estimates; Von mises expansions

Indexed keywords

EID: 0033248632     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. CABRERA, J., MEER, P. and LEUNG, H. (1994). Simulation methods for bias correction in ellipse estimation. In Proceedings of the Seattle Symposium on Computer Vision and Performance.
2. CABRERA, J. and MEER, P. (1996). Unbiased estimation of ellipses by bootstrapping. IEEE Trans. Pattern Analysis and Machine Intelligence 18 752-756.
3. CABRERA, J. and WATSON, G. S. (1997). Simulation methods for mean and median bias reduction in parametric estimation. J. Statist. Plann. Inference 57 143-152.
4. DEBICHE, M. G. and WATSON, G. S. (1996). Confidence limits and bias correction for estimating angles between directions with applications to palaeomagnetism. J. Geophysical Research 100 24, 405-24, 429.
5. EFRON, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia.
6. EFRON, B and TIBSHIRANI, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
7. FANKHAUSER, E. (1996). Etude du developpement de von Mises au deuxieme ordre. Diploma thesis. Ecole Polytechnique Federale, Lausanne, Switzerland.
8. FERNHOLZ, L. T. (1983). Von Mises Calculus for Statistical Functionals. Lecture Notes in Statist. 19. Springer, New York.
9. FERNHOLZ, L. T. (1996). On higher order von Mises expansions. Technical Report 96-04, Dept. Statistics, Temple Univ.
10. FILLIPOVA, A. A. (1962). Mises theorem on the asymptotic behavior of functionals of empirical distribution function and its statistical applications. Theory Prob. Appl. 7, pp. 24-57.
11. GATTO, R. and RONCHETTI, E. (1996). General saddlepoint approximations of marginal densities and tail probabilities. J. Amer. Statist. Assoc. 91 666-673.
12. HAMPEL, F. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69 383-393.
13. HAMPEL, F., RONCHETTI, E., ROUSSEEUW, P. and STAHEL, W. (1986). Robust Statistics. The Approach Based on the Influence Function. Wiley, New York.
14. HUBER, P. (1981). Robust Statistics. Wiley, New York.
15. REEDS, J. A. (1976). On the definition of von Mises functionals. Ph.D. dissertation, Harvard Univ.
16. ROUSSEEUW, P. and RONCHETTI, E. (1981). Influence curves of general statistics. J. Comput. Appl. Math. 7 161-166.
17. SCHUCANY, W. R., GRAY, H. R., AND OWEN, D. B. (1971). On Bias Reduction in Estimation. J. Amer. Statist. Assoc., 66, pp. 524-533.
18. VON MISES, R. (1947). On the asymptotic distribution of differentiable statistical functions. Ann. Math. Statist. 18, pp. 309-348.