SiZer Map for inference with additive models

Statistics and Computing

Volumn 18, Issue 3, 2008, Pages 297-312

  Gonzalez Manteiga W ^a   Martinez Miranda M D ^b   Raya Miranda, R ^b  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Interaction; Model checking; Residuals; Smoothing parameter; Test

Indexed keywords

EID: 45449087508     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-008-9057-z     Document Type: Article

References (49)

1. Azzalini, A., Bowman, A.W.: On the use of nonparametric regression for checking linear relationships. J. R. Stat. Soc. Ser. B 55, 549-557 (1993)
2. Barry, D.: Testing for additivity of a regression function. Ann. Stat. 21, 235-254 (1993)
3. Box, G.E.P., Draper, N.: Empirical Model-Building and Response Surfaces. Wiley, New York (1987)
4. Breiman, L., Friedman, J.H.: Estimating optimal transformations for multiple regression and correlation. J. Am. Stat. Assoc. 80, 580-598 (1985)
5. Chaudhuri, P., Marron, J.S.: SiZer for exploration of structures in curves. J. Am. Stat. Assoc. 94(447), 807-823 (1999)
6. Chaudhuri, P., Marron, J.S.: Scale space view of curve estimation. Ann. Stat. 28, 408-428 (2000)
7. Cleveland, W., Devlin, S.: Locally weighted regression: an approach to regression analysis by local fitting. J. Am. Stat. Assoc. 83, 596-610 (1988)
8. Cook, R.D., Weisberg, S.: Graphics for assessing the adequacy of regression models. J. Am. Stat. Assoc. 92(438), 490-499 (1997)
9. Cook, R.D., Weisberg, S.: Applied Regression Including Computing and Graphics. Wiley, New York (1999a)
10. Cook, R.D., Weisberg, S.: Graphs in statistical analysis: is the medium the message? Am. Stat. 53(1), 29-37 (1999b)
11. Derbort, S., Dette, H., Munk, A.: A test for additivity in nonparametric regression. Ann. Inst. Stat. Math. 54, 60-82 (2002)
12. Dette, H., Derbort, S.: Analysis of variance in nonparametric regression models. J. Multivar. Anal. 76, 110-137 (2001)
13. Dette, H., von Lieres und Wilkau, C.: Testing additivity by kernel-based methods-what is a reasonable test? Bernoulli 7, 669-697 (2001)
14. Dette, H., von Lieres und Wilkau, C., Sperlich, S.: A comparison of different nonparametric methods for inference on additive models. J. Nonparametr. Stat. 17, 57-81 (2005)
15. Eubank, R.L., Hart, J.D., Simpson, D.G., Stefanski, L.A.: Testing for additivity in nonparametric regression. Ann. Stat. 23, 1896-1920 (1995)
16. Fan, J., Jiang, J.: Nonparametric inferences for additive models. J. Am. Stat. Assoc. 100(471), 890-907 (2005)
17. Franklin, N.L., Pinchbeck, P.H., Popper, F.: A statistical approach to catalyst development, part I: the effect of process variables in the vapor phase oxidation of naphthalene. Trans. Inst. Chem. Eng. 34, 280-293 (1956)
18. Godtliebsen, F., Marron, J.S., Chaudhuri, P.: Significance in scale space for bivariate density estimation. J. Comput. Graph. Stat. 11, 1-21 (2002)
19. González-Manteiga, W., Cao, R.: Testing hypothesis of general linear model using nonparametric regression estimation. Test 2, 161-189 (1993)
20. Gozalo, P.L., Linton, O.B.: Testing additivity in generalized nonparametric regression with estimated parameters. J. Econom. 104, 1-48 (2001)
21. Gu, C.: Diagnostics for nonparametric regression models with additive terms. J. Am. Stat. Assoc. 87, 1051-1058 (1992)
22. Gustafson, P.: Bayessian regression modelling with interactions and smooth effects. J. Am. Stat. Assoc. 95, 795-806 (2000)
23. Hannig, J., Marron, J.S.: Advanced distribution theory for SiZer. J. Am. Stat. Assoc. 101, 484-499 (2006)
24. Härdle, W., Huet, S., Mammen, E., Sperlich, S.: Bootstrap inference in semiparametric generalized additive models. Econom. Theory 20, 265-300 (2004)
25. Härdle, W., Mammen, E.: Comparing nonparametric versus parametric regression fits. Ann. Stat. 21(4), 1926-1947 (1993)
26. Härdle, W., Sperlich, S., Spokoiny, V.: Structural tests in additive regression. J. Am. Stat. Assoc. 96, 1333-1347 (2001)
27. Hastie, T.J., Tibshirani, R.: Generalized additive models: some applications. J. Am. Stat. Assoc. 82, 371-386 (1987)
28. Hastie, T.J., Tibshirani, R.: Generalized Additive Models. Chapman & Hall, New York (1990)
29. Horowitz, J.L., Spokoiny, V.G.: An adaptative, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599-631 (2001)
30. Kim, C.S., Marron, J.S.: SiZer for jump detection. J. Nonparametr. Stat. 18, 13-20 (2006)
31. Li, R., Marron, J.S.: Local likelihood SiZer Map. Sankhya Indian J. Stat. 67, 476-498 (2005)
32. Lindeberg, T.: Scale Space Theory in Computer Vision. Kluwer Academic, Dordrecht (1994)
33. Marron, J.S., de Uña Álvarez, J.: SiZer for length biased, censored density and hazard estimation. J. Stat. Plan. Inference 121, 149-161 (2004)
34. Marron, J.S., Udina, F.: Interactive local bandwidth choice. Stat. Comput. 9, 101-110 (1999)
35. Marron, J.S., Zhang, J.T.: SiZer for smoothing splines. Comput. Stat. 20, 481-502 (2005)
36. Opsomer, J.D., Francisco-Fernández, M.: Finding local departures from a parametric model using nonparametric regression. Stat. Pap. (Published online: 9 January 2008)
37. Opsomer, J.D., Ruppert, D.: Fitting a bivariate additive model by local polynomial regression. Ann. Stat. 25, 186-211 (1997)
38. Opsomer, J.D., Ruppert, D.: A fully automated bandwidth selection method for fitting additive models. J. Am. Stat. Assoc. 93, 605-619 (1998)
39. Park, C., Kang, K.: SiZer analysis for the comparison of regression curves. Unpublished manuscript (2007)
40. Park, C., Marron, J.S., Rondonotti, V.: Dependent SiZer: goodness-of-fit tests for time series models. J. Appl. Stat. 31(8), 999-1017 (2004)
41. 2 pollution data. Stat. Comput. 15, 289-299 (2005)
42. Rondonotti, V., Marron, J.S., Park, C.: SiZer for time series: a new approach to the analysis of trends. Electron. J. Stat. 1, 268-289 (2007)
43. Ruppert, D., Wand, M.P., Carroll, R.J.: Semiparametric Regression. Cambridge University Press, Cambridge (2003)
44. Sperlich, S., Tjøstheim, D., Yang, L.: Nonparametric estimation and testing of interaction in additive models. Econom. Theory 18, 197-251 (2002)
45. Stone, C.J.: Additive regression and other nonparametric models. Ann. Stat. 13, 689-705 (1985)
46. Tukey, J.: On degree of freedom test for non-additivity. Biometrics 5, 232-242 (1949)
47. Yang, L., Sperlich, W., Härdle, W.: Derivative estimation and testing in generalized additive models. J. Stat. Plan. Inference 115, 521-542 (2003)
48. Zhang, C.M.: Adaptative tests of regression functions via multiscale generalized likelihood ratios. Can. J. Stat. 31, 151-171 (2003)
49. Zheng, J.X.: A consistent test of a functional form via nonparametric estimation techniques. J. Econom. 75, 263-289 (1996)