Abstract
Computation of one-sided simultaneous confidence bands is detailed for a simple linear regression under interval restrictions on the predictor variable, using a method due to Uusipaikka (1983,J. Amer. Statist. Assoc.,78, 638–644). The case of a single interval restriction is emphasized. A WWW-based applet for computing the bands is described.
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References
Bohrer, R. and Francis, G. K. (1972). Sharp one-sided confidence bounds for linear regression over intervals,Biometrika,59, 99–107.
Casella, G. and Strawderman, W. E. (1980). Confidence bands for linear regression with restricted predictor variables,J. Amer. Statist. Assoc.,75, 862–868.
Dalgård, C., Grandjean, P., Jørgensen, P. J. and Weihe, P. (1994). Mercury in the umbilical cord: Implications for risk assessment for Minamata disease,Environmental Health Perspectives,102, 548–550.
Halperin, M. and Gurian, J. (1968). Confidence bands in linear regression with constraints on the independent variables,J. Amer. Statist. Assoc.,63, 1020–1027.
Halperin, M., Rastogi, S. C., Ho, I. and Yang, Y. Y. (1967). Shorter confidence bands in linear regression,J. Amer. Statist. Assoc.,62, 1050–1068.
Hochberg, Y. and Quade, D. (1975). One-sided simultaneous confidence bands on regression surfaces with intercepts,J. Amer. Assoc.,70, 889–891.
Lane, T. P. and DuMouchel, W. H. (1994). Simultaneous confidence intervals in multiple regression,Amer. Statist.,48, 315–321.
Mahaffey, K. R. (2000). Recent advances in recognition of low-level methylmercury poisoning,Current Opinion in Neurology,13, 699–707.
Naiman, D. Q. (1983). Comparing Scheffé-type to constant-width confidence bounds in regression.J. Amer. Statist. Assoc.,78, 906–912.
Neter, J., Kutner, M. H., Nachtsheim, C. J. and Wasserman, W. (1996).Applied Linear Statistical Models, 4th ed, R.D. Irwin, Chicago.
Scheffé, H. (1953). A method for judging all contrasts in the analysis of variance,Biometrika,40, 87–104.
Shipp, A. M., Gentry, P. R., Lawrence, G., Van Landingham, C., Covington, T., Clewell, H. J., Gribben, K. and Crump, K. (2000). Determination of a site-specific reference dose for methylmercury for fish-eating populations,Toxicology and Industrial Health,16, 335–438.
Uusipaikka, E. (1983). Exact confidence bands for linear regression over intervals,J. Amer. Statist. Assoc.,78, 638–644.
West, R. W. and Ogden, R. T. (1997). Statistical analysis with WebStat, a Java applet for the World Wide Web,Journal of Statistical Software,2, p. 3.
Working, H. and Hotelling, H. (1929). Applications of the theory of error to the interpretation of trends,J. Amer. Statist. Assoc., Supplement toProceedings of the American Statistical Association,24, 73–85.
Wynn, H. P. and Bloomfield P. (1971). Simultaneous confidence bands in regression analysis.J. Roy. Statist. Soc. Ser. B,33, 202–217.
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Pan, W., Piegorsch, W.W. & West, R.W. Exact one-sided simultaneous confidence bands via Uusipaikka’s method. Ann Inst Stat Math 55, 243–250 (2003). https://doi.org/10.1007/BF02530497
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DOI: https://doi.org/10.1007/BF02530497