Bürmann expansion and test for additivity

Biometrika

Volumn 90, Issue 1, 2003, Pages 209-222

  Chan, K S ^a   Kristoffersen, A B ^b   Stenseth, N Chr ^b  

^a E11 SSH   (United States)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Alternating conditional expectations; Blowfly; Lagrange multiplier test; Nonlinear time series; Sieve; Volterra expansion

Indexed keywords

CHEN;

EID: 0038788171     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/90.1.209     Document Type: Article

References (31)

1. BILLINGSLEY, P. (1968). Convergence of Probability Measures. New York: Wiley.
2. BOX, G. E. P. & JENKINS, G. M. (1976). Time Series Analysis, Forecasting and Control. San Francisco: Holden-Day.
3. BREIMAN, L. & FRIEDMAN, J. H. (1985). Estimating optimal transformations for multiple regression and correlation (with Discussion). J. Am. Statist. Assoc. 80, 580-619.
4. BUJA, A., HASTIE, T. & TIBSHIRANI, R. (1989). Linear smoothers and additive models (with Discussion). Ann. Statist. 17, 453-555.
5. CHAN, K. S. & TONG, H. (1994). A note on noisy chaos. J. R. Statist. Soc. B 56, 301-11.
6. CHEN, R. & TSAY, R. (1993). Nonlinear additive ARX models. J. Am. Statist. Assoc. 88, 955-67.
7. CHEN, R., LIU, J. S. & TSAY, R. S. (1995). Additivity tests for nonlinear autoregression. Biometrika 82, 369-83.
8. CHEN, X. & SHEN, X. (1998). Sieve extremum estimates for weakly dependent data. Econometrica 66, 289-314.
9. CHENG, B. & TONG, H. (1992). Consistent nonparametric order determination and chaos (with Discussion). J. R. Statist. Soc. B 54, 427-74.
10. DOUKHAN, P., MASSART, P. & RIO, E. (1995). Invariance principles for absolutely regular empirical processes. Ann. Inst. Henri Poincaré 31, 393-427.
11. FOTOPOULOS, S. B. (2000). Invariance principles for deconvolving kernel density estimation for stationary sequences of random variables. J. Statist. Plan. Infer. 86, 31-50.
12. FRIEDMAN, J. H. (1991). Multivariate adaptive regression splines (with Discussion). Ann. Statist. 19, 1-141.
13. FRIEDMAN, J. H. & STUETZLE, W. (1981). Projection pursuit regression. J. Am. Statist. Assoc. 76, 817-23.
14. GRENANDER, U. (1981). Abstract Inference. New York: Wiley.
15. HASTIE, T. & TIBSHIRANI, R. J. (1990). Generalized Additive Models. London: Chapman & Hall.
16. LEWIS, P. A. W. & STEVENS, J. G. (1991). Nonlinear modeling of time series using multivariate adaptive regression splines (MARS). J. Am. Statist. Assoc. 86, 864-77.
17. LINGJæRDE, O. C., STENSETH, N. C., KRISTOFFERSEN, A. B., SMITH, R. H., MOE, J., READ, J. M., DANIELS, S. & SIMKISS, K. (2001). Exploring non-linearities in the stage-specific density-dependent structure of experimental blowfly populations using non-parametric additive modelling. Ecology 82, 2645-58.
18. LINTON, O. (2000). Efficient estimation of generalized additive nonparametric regression models. Economet. Theory 16, 502-23.
19. LINTON, O. & NIELSEN, J. P. (1995). A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82, 93-100.
20. MAMMEN, E., LINTON, O. & NIELSEN, J. (1999). The existence and asymptotic properties of a backfilling projection algorithm under weak conditions. Ann. Statist. 27, 1443-90.
21. NEWEY, W. K. (1994). Kernel estimation of partial means. Economet. Theory 10, 233-53.
22. POWELL, J. L., STOCK, J. H. & STOKER, T. M. (1989). Semiparametric estimation of index coefficients. Econometrica 57, 1403-30.
23. RIO, E. (1993). Covariance inequalities for strongly mixing processes. Ann. Inst. Henri Poincaré 29, 587-97.
24. SHEN, X. & WONG, W. H. (1994). Convergence rate of sieve estimates. Ann. Statist. 22, 580-615.
25. TJØSTHEIM, D. & AUESTAD, B. (1990). Identification of nonlinear time series: First order characterization and order determination. Biometrika 77, 669-87.
26. TJØSTHEIM, D. & AUESTAD, B. (1994). Nonparametric identification of nonlinear time series: Projections. J. Am. Statist. Assoc. 89, 1398-409.
27. TONG, H. (1990). Non-linear Time Series: A Dynamical System Approach. Oxford University Press: Oxford.
28. TONG, H. (1995). A personal overview of nonlinear time-series analysis from a chaos perspective. Scand. J. Statist. 22, 399-421.
29. VOLTERRA, V. (1930). Theory of Functional. London: Blackie.
30. WHITTAKER, E. T. & WATSON, G. B. (1927). A Course of Modern Analysis, 4th ed. New York: Cambridge University Press.
31. XIA, Y., TONG, H. & LI, W. K. (1999). On extended partially linear single-index models. Biometrika 86, 831-42.