Statistical inferences for linear regression models when the covariates have functional relationships: Polynomial regression

Journal of Statistical Computation and Simulation

Volumn 78, Issue 4, 2008, Pages 315-324

  Liu, Wei ^a   Wynn, H P ^b   Hayter, A J ^c  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Confidence bands; F tests; Linear regression; Polynomial regression; Simultaneous inference; Statistical simulation

Indexed keywords

EID: 41549110727     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949650601100981     Document Type: Article

References (16)

1. Kleinbaum, D.G., Kupper, L.L., Muller, K.E. and Nizam, A., 1998, Applied Regression Analysis and Other Multivariable. Methods (3rd edn) (Duxbury Press).
2. Montgomery, D.C., 1991, Design and Analysis of Experiments (3rd edn) (Wiley).
3. Draper, N. and Smith, H., 1998, Applied Linear Regression (3rd edn.) (Wiley).
4. Dette, H. and Kwiecien, R., 2005, Finite sample performance of sequential designs for model identification. Journal of Statistical Computation and Simulation, 75(6), 477-495.
5. Scheffé, H., 1959, The Analysis of Variance (Wiley).
6. Roy, S.N. and Bose, R.C., 1953, Simultaneous confidence interval estimation. Annals of Mathematical Statististics, 24, 513-536.
7. Scheffe, H., 1953, A method for judging all contrasts in the analysis of variance. Biometrika, 41, 153-169.
8. Kosorok, M.R. and Qu, R., 1999, Exact simultaneous confidence bands for a collection, of univariate polynomials in regression analysis. Statistics in Medicine, 18, 613-620.
9. Liu, W., Jamshidian, M. and Zhang, Y., 2004, Multiple comparison of several regression models. Journal of American Statistical Association, 99, 395-403.
10. Liu, W., Jamshidian, M., Zhang, Y. and Donnelly, J., 2005, Simulation-based simultaneous confidence bands for a multiple linear regression model when the covariates are constrained. Journal of Computational and Graphical Statistics, 14(2), 459-484.
11. Edwards, D. and Berry, J.J., 1987, The efficiency of simulation-based multiple comparisons. Biometrics, 43, 913-928.
12. Selvin, S., 1998, Modern Applied Biostatistical Methods Using S-Plus (Oxford University Press).
13. Wynn, H.P. and Bloomfield, P., 1971, Simultaneous confidence bands in regression analysis. Journal of Royal Statistical Society (B), 33, 202-217.
14. Naiman, D.Q., 1986, Conservative confidence regions in curvilinear regression. Annals of Mathematical Statistics, 14, 896-906.
15. Wynn, H.P., 1984, An exact confidence band for one-dimensional polynomial regression. Biometrika, 71, 375-379.
16. Spurrier, J.D., 1993, Comparison of simultaneous confidence bands for quadratic regression over a finite interval. Technometrics, 35, 315-320.