Smoothing-based lack-of-fit tests: Variations on a theme

Journal of Nonparametric Statistics

Volumn 7, Issue 1, 1996, Pages 1-22

  Kuchibhatla, Maragatha ^a   Hart, Jeffrey D ^a  

^a DUKE UNIVERSITY MEDICAL CENTER   (United States)

Author keywords

Automated smoothing; Fourier series; Nonparametric regression; Parametric models

Indexed keywords

EID: 0002546986     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259608832685     Document Type: Article

References (31)

1. Azzalini, A. Bowman, A. W. and Härdie, W. (1989), "On the Use of Nonparametric Regression for Model Checking," Biometrika, 76, 1-11.
2. Azzalini, A and Bowman, A (1993), "On the Use of Nonparametric Regression for Checking Linear Relationships," Journal of the Royal Statistical Society B, 55, 549-557.
3. Barry, R. and Hartigan, J. A. (1990), "An Omnibus Test for Departures from Constant Mean," Annals of Statistics, 18, 1340-1357.
4. Bhattacharya, P. K. (1974), "Convergence of Sample Paths of Normalized Sums of Induced Order Statistics," Annals of Statistics, 2, 1034-1039.
5. Bhattacharya, R. N. and Ranga Rao, R. (1986), Normal Approximation and Asymptotic Expansions, New York: John Wiley.
6. Butzer, P. L. and Nessel, R. J. (1971), Fourier Analysis and Approximation, New York and London: Academic press.
7. Carroll, R. J. and Ruppert, D. (1988), Transformation and Weighting in Regression, New York and London: Chapman and Hall.
8. Chen, J.-C. (1994),"Testing Goodness of Fit of Polynomial Models via Spline Smoothing Techniques," Statistics and Probability Letters, 19, 65-76.
9. Delgado, M. A. (1993),"Testing the Equality of Nonparametric Regression Curves," Statistics and Probability Letters, 17, 199-204.
10. Diggle, P. (1990), Time Series, A Biostatistical Introduction, Oxford: Clarendon.
11. Eubank, R. L. and Spiegelman, C. H. (1990), "Testing the Goodness-of-Fit of a Linear Model via Nonparametric Regression Techniques," Journal of American Statistical Association, 85, 387-392.
12. Eubank, R. L. and Hart, J. D. (1992), "Testing Goodness-of-Fit in Regression via Order Selection Criteria," Annals of Statistics, 20, 1412-1425.
13. Eubank, R. L. and Hart, J. D. (1993), "Commonality of Cusum, von Neumann and Smoothing-Based Goodness-of-Fit Tests," Biometrika, 80, 89-98.
14. Eubank, R. L. Hart, J. D. Simpson, D. G. and Stefanski, L. A. (1996),"Testing for Additivity in Nonparametric Regression," Annals of Statistics, to appear.
15. Firth, D. Glosup, J. and Hinkley, D. V. (1991), "Model Checking With Nonparametric Curves," Biometrika, 78, 245-252.
16. Gasser, T. Sroka, L. and Jennen-Steinmetz, C. (1986),"Residual Variance and Residual Pattern in Nonlinear Regression," Biometrika, 73, 625-633.
17. Grenander, U. and Rosenblatt, M. (1957), Statistical Analysis of Stationary Time Series, New York: John Wiley.
18. Hall, P. (1983),"Measuring the Efficiency of Trigonometric Series Estimates of a Density," Journal of Multivariate Analysis, 13, 234-256.
19. Hall, P. and Hart, J. D. (1990), "Bootstrap Test for Difference Between Means in Nonparametric Regression," Journal of the American Statistical Association, 85, 1039-1049.
20. Hall, P. Kay, J. W. and Titterington, D. M. (1990), "Asymptotically Optimal Difference Based Estimation of Variance in Nonparametric Regression," Biometrika, 77, 521-528.
21. Hardie, W. and Mammen, E.(1993), "Comparing Nonparametric Versus Parametric Regression Fits," Annals of Statistics, 21, 1926-1947.
22. Hart, J. D. and Wehrly, T. E. (1992), "Kernel Regression When the Boundary Region is Large, With an Application to Testing the Adequacy of Polynomial Models," Journal of the American Statistical Association, 87, 1018-1024.
23. King, E. Hart, J. D. and Wehrly, T. E. (1991), "A Test of Equality of Two Regression Curves using Linear Smoothers," Statistics and Probability Letters, 12, 239-247.
24. Munson, P. J. and Jernigan, R. W. (1989), "A Cubic Spline Extension of the Durbin-Watson Test," Biometrika, 76, 39-47.
25. Neumann, J von (1941), "Distribution of the Ratio of the Mean Squared Successive Differences to the Variance, "Annals of Mathematical Statistics, 12, 367-395.
26. Priestley, M. B. (1981), Spectral Analysis and Time Series, London: Academic Press.
27. Ramachandran, M. (1993),"Testing Goodness of Fit Using Nonparametric Techniques," Ph.D. dissertation, Department of Statistics, Texas A and M University.
28. Rao, C. R. (1973), Linear Statistical Inference and Its Applications, New York: John Wiley.
29. Serfling, R. J. (1980), Approximation Theorems of Mathematical Statistics, New York: John Wiley.
30. Spitzer, F. (1956), "A Combinatorial Lemma and its Applications to Probability Theory," Transactions of American Mathematical Society, 82, 323-339.
31. Staniswalis, J. and Severini, T. A. (1991), "Diagnostics for Assessing Regression Models," Journal of the American Statistical Association, 86, 684-692.