Testing strict monotonicity in nonparametric regression

Mathematical Methods of Statistics

Volumn 16, Issue 2, 2007, Pages 110-123

  Birke, M ^a   Dette, H ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

goodness of fit test; nonparametric regression; strictly monotone regression

Indexed keywords

EID: 49649124486     PISSN: 10665307     EISSN: 19348045     Source Type: Journal    
DOI: 10.3103/S1066530707020032     Document Type: Article

References (22)

1. Y. Baraud, S. Huet, B. Laurent, "Adaptive tests of qualitative hypotheses", ESAIM, Probab. Statist. 7, 147-159 (2003).
2. A. W. Bowman, M. C. Jones, and I. Gijbels, "Testing monotonicity of regression", J. Computational and Graphical Statist. 7, 489-500 (1998).
3. H. D. Brunk, "Maximum likelihood estimates of monotone parameters," Ann. Math. Statist. 26, 607-616 (1955).
4. H. Dette, N. Neumeyer, and K. F. Pilz, "A simple nonparametric estimator of a monotone regression function", Bernoulli 12, 469-490 (2006).
5. 2 point of view in testing monotone regression", J. Nonparam. Statist. 17, 135-153 (2006).
6. C. Durot, "A Kolmogorov-type test for monotonicity of regression", Statist. Probab. Lett. 63, 425-433 (2003).
7. J. Fan and I. Gijbels, Local Polynomial Modelling and Its Applications (Chapman and Hall, London, 1997).
8. J. Friedman and R. Tibshirani, "The monotone smoothing of scatterplots", Technometrics 26, 243-250 (1984).
9. S. Ghosal, A. Sen, A. W. van der Vaart, "Testing monotonicity of regression", Ann. Statist. 28, 1054-1082 (2000).
10. I. Gijbels, P. Hall, M. C. Jones, and I. Koch, "Tests for monotonicity of a regression mean with guaranteed level", Biometrika 87, 663-673 (2000).
11. P. Hall, "Integrated square error properties of kernel estimators of regression functions", Ann. Statist. 12, 241-260 (1984).
12. P. Hall and N. E. Heckman, "Testing for monotonicity of a regression mean by calibrating for linear functions", Ann. Statist. 28, 20-39 (2000).
13. P. Hall and L.-S. Huang, "Nonparametric kernel regression subject to monotonicity constraints", Ann. Statist. 29, 624-647 (2001).
14. Y. P. Mack and B. W. Silverman, "Weak and strong uniform consistency of kernel regression estimates", Z. Wahrsch. verw. Gebiete 61, 405-415 (1982).
15. E. Mammen, "Estimating a smooth monotone regression function", Ann. Statist. 19, 724-740 (1991).
16. E. Mammen, "Bootstrap and wild bootstrap for high dimensional linear models", Ann. Statist. 21, 255-285 (1993).
17. H. Mukerjee, "Monotone nonparametric regression", Ann. Statist. 16, 741-750 (1988).
18. J. O. Ramsay, "Estimating smooth monotone functions", J. Roy. Statist. Soc., Ser. B 60, 365-375 (1998).
19. W. Schlee (1982). "Nonparametric tests of the monotony and convexity of regression. Nonparametric statistical inference", in Colloq. Math. Soc. Janos Bolyai 32 (Budapest, 1980) Vol. II, pp. 823-836.
20. R. J. Serfling, Approximation Theorems of Mathematical Statistics (Wiley, New York, 1980).
21. B. W. Silverman, "Using kernel density estimates to investigate multimodality", J. Roy. Statist. Soc. Ser. B 43, 97-99 (1981).
22. C. F. Y. Wu, "Jacknife, bootstrap and other resampling methods in regression analysis", Am. Statist. 14, 1261-1350 (1986).