Confidence regions for the set of global maximizers of nonparametrically estimated curves

Journal of Statistical Planning and Inference

Volumn 82, Issue 1-2, 1999, Pages 237-250

  Futschik, A ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033444768     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(99)00046-4     Document Type: Article

References (25)

1. Abramovich, F., Benjamini, Y., 1996. Adaptive thresholding of wavelet coefficients. Comput. Statist. Data Anal. 22, 351-362.
2. Eubank, R.L., Speckman, P.L., 1993. Confidence bands in nonparametric regression. J. Amer. Statist. Assoc. 88, 1287-1301.
3. Eubank, R.L., Thomas, W., 1993. Detecting heteroscedasticity in non-parametric regression. J. Amer. Statist. Assoc. 88, 1287-1301.
4. Fan, J., Gijbels, I., 1996. Local Polynomial Modelling and its Applications. Chapman & Hall, London.
5. Fan, J., Gijbels, I., Hu, T.-C., Huang, L.-S., 1996. An asymptotic study of variable bandwidth selection for local polynomial regression with application to density estimation. Statist. Sin. 6.
6. Grenander, U., 1981. Abstract Inference. Wiley, New York.
7. Gupta, S.S., Huang, D.-Y., 1976. Selection procedures for the means and variances of normal populations: Unequal sample size case. Sankhya B 38, 112-128.
8. Hall, P., Titterington, D.M., 1988. On confidence bands in nonparametric density estimation and regression. J. Multivariate Anal. 27, 228-254.
9. Härdle, W., 1990. Applied Nonparametric Regression. Cambridge Univ. Press, Cambridge.
10. Härdle, W., 1991. Asymptotic maximal deviation of M-smoothers. Ann. Statist. 19, 778-796.
11. Härdle, W.K., Nixdorf, R., 1987. Nonparametric sequential estimation of zeros and extrema of regression functions. IEEE Trans. Inform. Theory 333, 3367-3372.
12. Hengartner, N.W., Stark, P.B., 1995. Finite-sample confidence envelopes for shape-restricted densities. Ann. Statist. 23, 525-550.
13. Holm, S., 1979. A simple sequentially rejective multiple test procedure. Scand. J. Statist. 6, 65-70.
14. Hsu, J.C., 1992. Stepwise multiple comparison with the best. J. Statist. Plann. Inference 33, 197-204.
15. Hsu, J.C., 1996. Multiple Comparisons: Theory and Methods. Chapman & Hall, London.
16. Knafl, G., Sacks, J., Ylvisaker, D., 1985. Confidence bands for regression functions. J. Amer. Statist. Assoc. 80, 683-691.
17. Minotte, M.C., 1997. Nonparametric testing of the existence of modes. Ann. Statist. 25, 1646-1660.
18. Müller, H.G., 1985. Kernel estimators of zeros and of location and size of extrema of regression functions. Scand. J. Statist. 12, 221-232.
19. Müller, H.G., 1987. Weighted local regression and kernel methods for nonparametric curve fitting. J. Amer. Statist. Assoc. 82, 231-238.
20. Müller, H.G., 1989. Adaptive nonparametric peak estimation. Scand. J. Statist. 17, 1053-1069.
21. Nazin, A.V., Polyak, B.T., Tsybakov, A.B., 1990. Passive stochastic approximation. Preprint. Inst. of Control Science, Acad. of Sci. USSR. J. Amer. Statist. Assoc. 88, 1287-1301.
22. Reiss, R.-D., 1989. Approximate Distributions of Order Statistics. Springer, New York.
23. Rice, J., 1984. Bandwidth choice for nonparametric regression. Ann. Statist. 12, 1215-1230.
24. Serfling, R.J., 1980. Approximation Theorems of Mathematical Statistics. Wiley, New York.
25. Stone, C.J., Hansen, M.H., Kooperberg, Ch., Truong, Y.K., 1997. Polynomial splines and their tensor products in extended linear modeling. (With discussion.) Ann. Statist. 25, 1371-1471 (1980).