Serial and nonserial sign-and-rank statistics: Asymptotic representation and asymptotic normality

Annals of Statistics

Volumn 34, Issue 1, 2006, Pages 254-289

  Hallin, Marc ^a   Vermandele, Catherine ^a   Werker, Bas ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b TILBURG UNIVERSITY   (Netherlands)

Author keywords

Hajek representation; Maximal invariant; Median regression; Median restrictions; Ranks; Signs

Indexed keywords

EID: 33744826550     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000769     Document Type: Article

References (21)

1. AZZALINI, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12 171-178. MR0808153
2. DUFOUR, J.-M., LEPAGE, Y. and ZEIDAN, H. (1982). Nonparametric testing for time series: A bibliography. Canad. J. Statist. 10 1-38. MR0660939
3. HÁJEK, J. and ŠIDÁK, Z. (1967). Theory of Rank Tests. Academic Press, New York. MR0229351
4. HÁJEK, J., ŠIDÁK, Z. and SEN, P. K. (1999). Theory of Rank Tests, 2nd ed. Academic Press, San Diego. MR 1680991
5. HALLIN, M., INGENBLEEK, J.-F. and PURI, M. L. (1985). Linear serial rank tests for randomness against ARMA alternatives. Ann. Statist. 13 1156-1181. MR0803764
6. HALLIN, M. and PURI, M. L. (1988). Optimal rank-based procedures for time-series analysis: Testing an ARMA model against other ARMA models. Ann. Statist. 16 402-432. MR0924878
7. HALLIN, M. and PURI, M. L. (1991). Time-series analysis via rank-order theory: Signed-rank tests for ARMA models. J. Multivariate Anal. 39 1-29. MR1128669
8. HALLIN, M. and PURI, M. L. (1992). Rank tests for time series analysis: A survey. In New Directions in Time Series Analysis. Part 1 (D. Brillinger, P. Caines, J. Geweke, E. Parzen. M. Rosenblatt and M. S. Taqqu, eds.) 111-153. Springer, New York. MR1235582
9. HALLIN, M. and PURI, M. L. (1994). Aligned rank tests for linear models with autocorrelated error terms. J. Multivariate Anal. 50 175-237. MR 1293044
10. HALLIN, M., VERMANDELE, C. and WERKER, B. J. M. (2004). Semiparametrically efficient inference based on signs and ranks for median restricted models. Technical Report 0403. Tilburg Univ.
11. HALLIN, M. and WERKER, B. J. M. (2003). Semi-parametric efficiency, distribution-freeness and invariance. Bernoulli 9 137-165. MR1963675
12. HOROWITZ, J. L. and SPOKOINY, V. G. (2002). An adaptive rate-optimal test of linearity for median regression models. J. Amer. Statist. Assoc. 97 822-835. MR1941412
13. HUŠKOVÁ, M. (1970). Asymptotic distribution of simple linear rank statistics for testing symmetry. Z. Wahrsch. Verw. Gebiete 14 308-322. MR0277050
14. JUNG, S.-H. (1996). Quasi-likelihood for median regression models. J. Amer. Statist. Assoc. 91 251-257. MR1394079
15. KOENKER, R. (2000). Galton, Edgeworth, Frisch, and prospects for quantite regression in econometrics. J. Econometrics 95 347-374. MR 1752335
16. LE CAM, L. (1986). Asymptotic Methods in Statistical Decision Theory. Springer, New York. MR0856411
17. MCKEAGUE, I. W., SUBRAMANIAN, S. B. and SUN, Y. Q. (2001). Median regression and the missing information principle. J. Nonparametr. Statist. 13 709-727. MR1931164
18. PURI, M. L. and SEN, P. K. (1985). Nonparametric Methods in General Linear Models. Wiley, New York. MR0794309
19. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York. MR0595165
20. YOSHIHARA, K.-I. (1976). Limiting behaviour of U-statistics for stationary absolutely regular processes. Z. Wahrsch. Verw. Gebiete 35 237-252. MR0418179
21. ZHAO, Q. S. (2001). Asymptotically efficient median regression in the presence of heteroskedasticity of unknown form. Econometric Theory 17 765-784, MR 1862375