Maximal type test statistics based on conditional processes

Journal of Statistical Planning and Inference

Volumn 53, Issue 1, 1996, Pages 1-19

  Beirlant, Jan ^a   Einmahl, John H J ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Empirical processes; Extreme value theory; Non parametric regression

Indexed keywords

EID: 0030210693     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-3758(96)00135-8     Document Type: Article

References (18)

1. Bhattacharya, P.K. and A.K. Gangopadhyay (1990). Kernel and nearest-neighbor estimation of a conditional quantile. Ann. Statist. 18, 1400-1415.
2. Cressie, N. (1980). The asymptotic distribution of the scan statistic under uniformity. Ann. Probab. 8, 828-840.
3. Cressie, N. (1987). Using the scan statistic to test for uniformity. In: Goodness-of-Fit, Colloquia Mathematica Societatis Janós Bolyai 45, North-Holland, Amsterdam, 87-100.
4. Csörgo, M. and P. Révész (1981). Strong Approximations in Probability and Statistics. Academic Press, New York.
5. Deheuvels, P. and P. Révész (1987). Weak laws for the increments of Wiener processes, Brownian bridges, empirical processes and partial sums of i.i.d. rv's. In: M.L. Puri et al., Eds., Mathematical Statistics and Probability Theory, Vol. A. Reidel, Dordrecht, 69-88.
6. Dijkstra, J.B., T.J.M. Rietjens and F.W. Steutel (1984). A simple test for uniformity. Statist. Neerlandica 38, 33-44.
7. Einmahl, J.H.J. and D.M. Mason (1992). Generalized quantile processes. Ann. Statist. 20, 1062-1078.
8. Grübel, R. (1988). The length of the shorth. Ann. Statist. 16, 619-628.
9. Kiefer, J. (1959). K-sample analogues of the Kolmogorov-Smirnov and Cramér-von Mises tests. Ann. Math. Statist. 30, 420-447.
10. Kim, J. and D. Pollard (1990). Cube root asymptotics. Ann. Statist. 18, 191-219.
11. Komlós, J., P. Major and G. Tusnády (1975). An approximation of partial sums of independent RV's and the sample DF. I. Z. Wahrsch. Verw. Gebiete 32, 111-131.
12. Naus, J.I. (1966). A power comparison of two tests of nonrandom clustering. Technometrics 8, 493-517.
13. Naus, J.I. (1982). Approximations for distributions of scan statistics. J. Amer. Statist. Assoc. 77, 177-183.
14. Resnick, S.I. (1987). Extreme Values, Regular Variation, and Point Processes. Springer, New York.
15. Rousseeuw, P. (1984). Least median of squares regression. J. Amer. Statist. Assoc. 79, 871-880.
16. Rousseeuw, P. and A. Leroy (1988). A robust scale estimator based on the shortest half. Statist. Neerlandica 42, 103-116.
17. Ruymgaart, F.H. (1994). Conditional empirical, quantile and difference processes for a large class of time series with applications. J. Statist. Plann. Inference 40, 15-31.
18. Stute, W. (1986). On almost sure convergence of conditional empirical distribution functions. Ann. Probab. 14, 891-901.