Advertisement

Scope of the Monograph

  • Erkki P. Liski
  • Nripes K. Mandal
  • Kirti R. Shah
  • Bikas K. Sinha
Part of the Lecture Notes in Statistics book series (LNS, volume 163)

Abstract

This monograph covers recent research findings in certain areas of discrete and continuous optimal designs, largely touching upon the interests of the authors spanning over the past ten years or so. We hope that the reader will find this useful for pursuing further research on these topics.

Keywords

Polynomial Regression Information Matrix Random Coefficient Growth Curve Model Polynomial Regression Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abt, M., Gaffke, N., Liski, E. P. and Sinha, Bikas K. (1998). Optimal de-signs in crowth curve models: Part II. Correlated model for quadratic growth: Optimal designs for slope parameter estimation and growth prediction. Journal of Statistical Planning and Inference 67, 287–296.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Abt, M., Liski, Å. Ð, Mandal N. K. and Sinha, Bikas K. (1997). Optimal design in crowth curve models: Part I. Correlated model for linear growth: Optimal designs for slope parameter estimation and growth prediction. Journal of Statistical Planning and Inference 64, 141–150.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Agrawal, H. L. (1966). Some systematic methods of construction of designs for two-way elimination of heterogeneity. Calcutta Statistical Association Bulletin 15, 93–108.MathSciNetzbMATHGoogle Scholar
  4. Atkinson, A. C. and Donev, A. N. (1992). Optimum experimental design. Oxford: Oxford University Press.Google Scholar
  5. Baltagi, B. H. (1995). Econometric analysis of panel data. Wiley, New York.zbMATHGoogle Scholar
  6. Box, G. Å. P. (1985). The Collected works of George E. P. Box (Eds. G. C. Tiao, C. W. J. Granger, I. Guttman, B. H. Margolin, R. D. Snee, S. M. Stigler). Wadsworth, Belmont, CA.zbMATHGoogle Scholar
  7. Box, G. E. P. and Draper, N. R. (1959). A basis for the selection of a response surface design. Journal of the American Statistical Association 54, 622–654.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Box, G. Å. P. and Draper, N. R. (1987). Empirical model-building and response surfaces. Wiley, New York.zbMATHGoogle Scholar
  9. Box, G. Å. P. and Wilson, K. B. (1951). On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society Series B 13, 1–38.MathSciNetGoogle Scholar
  10. Bradley, R. A. and Yeh, C. M. (1980). Trend-free block designs: Theory. Annals of Statistics 8, 883–893.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Carter, R. L. and Yang, M. C. K. (1986). Large sample inference in random coefficient regression models. Communications in Statistics-Theory Methods 15, 2507–2525.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Chaloner, K. and Verdinelli, I. (1995). Bayesian experimental design: A review. Statistical Science 10, 273–304.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Chernoff, H. (1953). Locally optimal designs for estimating parameters. Annals of Mathematical Statistics 24, 586–602.MathSciNetzbMATHCrossRefGoogle Scholar
  14. de la Garza, A. (1954). Spacing of information in polynomial regression. Annals of Mathematical Statistics 25 , 123–130.MathSciNetzbMATHCrossRefGoogle Scholar
  15. Diggle, P. J. (1994). analysis of longitudinal data. Oxford: Clarendon Press.Google Scholar
  16. Elfving, G. (1952). Optimum allocation in linear regression theory. Annals of Mathematical Statistics 23, 255–262.MathSciNetzbMATHCrossRefGoogle Scholar
  17. Elfving, G. (1955). Geometric allocation theory. Skandinavisk Aktuarietid-skrift 37, 170–190.MathSciNetGoogle Scholar
  18. Elfving, G. (1956). Selection of nonrepeatable observations for estimation. Proceedings of the 3rd Berkeley Symposium of Mathematical Statistics and Probability 1, 69–75.MathSciNetGoogle Scholar
  19. Elfving, G. (1959). Design of linear experiments. Probability and statistics. The Harald Cramér Volume (ed. by Ulf Grenander), 58–74. Wiley, New York.Google Scholar
  20. Elston, R. C. and Grizzle, J. F. (1962). Estimation of time response curves and their confidence bands. Biometrics 18, 148–159.zbMATHCrossRefGoogle Scholar
  21. Fedorov, V. V. (1972). Theory of optimal experiments. Academic Press, New York.Google Scholar
  22. Gafïke, N. and Heiligers, B. (1996). Second order methods for solving extremum problems from optimal linear regression designs. Optimization 36, 41–57.MathSciNetCrossRefGoogle Scholar
  23. Ghosh, S. and Rao, C. R. (1996, eds.). Handbook of Statistics 13. Elsevier, Amsterdam.Google Scholar
  24. Grizzle, J. F. and Allen, D. M. (1969). Analysis of growth and dose response curves. Biometrics 25, 357–382.CrossRefGoogle Scholar
  25. Guest, P. G. (1958). The spacing of observations in polynomial regression. Annals of Mathematical Statistics 29, 294–299.MathSciNetzbMATHCrossRefGoogle Scholar
  26. Hoel, P. G. (1958). Effiency problems in polynomial estimation. Annals of Mathematical Statistics 29, 1134–1145.MathSciNetzbMATHCrossRefGoogle Scholar
  27. Hoel P. G. (1965). Minimax designs in two dimensional regression. Annals of Mathematical Statistics. 36, 1097–1106.MathSciNetzbMATHCrossRefGoogle Scholar
  28. Jennrich, R. I. and Schluchter, M. D. (1986). Unbalanced repeated measure models with structured covariance matrices. Biometrics 42, 805–820.MathSciNetzbMATHCrossRefGoogle Scholar
  29. Jones, R. H. and Ackerson, C. M. (1990). Serial correlation in equally spaced longitudinal data. Biometrika 77, 721–731.MathSciNetCrossRefGoogle Scholar
  30. Jones, R. H. and Boadi-Boateng, F. (1991). Unequally spaced longitudinal data with AR(1) serial correlation. Biometrics 47, 161–175.CrossRefGoogle Scholar
  31. Karlin, S. and Studden, W. J. (1966). Optimal experimental designs. Annals of Mathematical Statistics 37, 783–815.MathSciNetzbMATHCrossRefGoogle Scholar
  32. Khatri, C. G. (1966). A note on a MANOVA model applied to problems in growth curves. Annals of the Institute of Statistical Mathe-matics 18, 75–86.MathSciNetzbMATHCrossRefGoogle Scholar
  33. Kiefer, J. C. (1961). Optimum designs in regression problems, II. Annals of Mathematical Statistics 32, 298–325.MathSciNetzbMATHCrossRefGoogle Scholar
  34. Kiefer, J. C. (1962). An extremum result. Canadian Journal of Mathematics 14, 597–601.MathSciNetzbMATHCrossRefGoogle Scholar
  35. Kiefer, J. C. (1974). General equivalence theory for optimum designs (approximate theory). Annals of Statistics 2, 849–879.MathSciNetzbMATHCrossRefGoogle Scholar
  36. Kiefer, J. C. (1975). Construction and optimality of generalized Youden designs. In J. N. Srivastava Ed. A Survey of Statistical Design and Linear Models. North-Holland, Amsterdam, 333–353.Google Scholar
  37. Kiefer, J. C. and Wolfowitz J. (1959). Optimum designs in regression prob-lems. Annals of Mathematical Statistics 30, 271–294.MathSciNetzbMATHCrossRefGoogle Scholar
  38. Kiefer, J. C. and Wolfowitz J. (1960). The eiquivalence of two extremum problems. Canadian Journal of Mathematics 12, 363–366.MathSciNetzbMATHCrossRefGoogle Scholar
  39. Laird, N. M., Lange, N. and Stram, D. (1987). Maximum likelihood com-putations with repeated measures: Application of the EM algorithm. Journal of the Amererican Statististical Association 82, 97–105.MathSciNetzbMATHCrossRefGoogle Scholar
  40. Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963–974.zbMATHCrossRefGoogle Scholar
  41. Lindley, D. V. (1956). On a measure of the information provided by an experiment. Annals of Mathematical Statistics 27, 986–1005.MathSciNetzbMATHCrossRefGoogle Scholar
  42. Lindsay, J. K. (1993). Models for repeated measurements. Oxford: Clarendon Press.Google Scholar
  43. Lindstrom, M. J. and Bates, D. M. (1988). Newton-Rapson and EM al-gorithms for linear mixed-effects model for repeated-measures data. Journal of the Amererican Statististical Association 83, 1014–1022.MathSciNetzbMATHGoogle Scholar
  44. Liski, E. P. and Nummi, T. (1995a). Prediction and inverse estimation in repeated-measures models. Journal of Statistical Planning and Inference 47, 141–151.zbMATHCrossRefGoogle Scholar
  45. Liski, E. P. and Nummi, T. (1995b). Prediction of tree stems to improve efficiency in automatized harvesting of forests. Scandinavian Journal of Statistics 22, 255–259.zbMATHGoogle Scholar
  46. Liski, E. P. and Nummi, T. (1996a). The marking for bucking under uncertainty in automatic harvesting of forests. The International Journal of Production Economics 46–47, 373-385.Google Scholar
  47. Liski, E. P. and Nummi, T. (1996b). Prediction in repeated-measures mod-els with engineering applications. Technometrics 38, 25–36.MathSciNetzbMATHCrossRefGoogle Scholar
  48. Liski, E. P., Luoma, A. and Sinha, Bikas K. (1996). Optimal designs in a random coefficient linear growth curve model. Calcutta Statistical Association Bulletin 46, 211–229.MathSciNetzbMATHGoogle Scholar
  49. Liski, E. P., Luoma, A., Mandal, N. K. and Sinha, Bikas K. (1998). Optimal designs for prediction in random coefficient linear regression models. Journal of Combinatorics, Information and System Sciences (J. N. Srivastava Felicitation Volume), 23(1-4), 1–16.MathSciNetzbMATHGoogle Scholar
  50. Lopes Troya, J. (1982). Optimal designs for covariate models. Journal of Statistical Planning and Inference 6, 373–419.MathSciNetzbMATHCrossRefGoogle Scholar
  51. Minkin, S. (1993). Experimental design for clonogenic assay in chemotherapy. Journal of the Americal Statistical Association 88, 410–420.MathSciNetCrossRefGoogle Scholar
  52. Morgan, J. P. (1996). Nested designs. In S. Ghosh and C. R. Rao (ed.) Handbook of Statistics 13, 939–976.Google Scholar
  53. Ozawa, K., Jimbo, M., Kageyama, S. and Mejza, S. (2001). Optimality and construction of incomplete split-block designs. To appear in Journal of Statistical Planning and Inference.Google Scholar
  54. Pázman, A. (1986). Foundations of optimum experimental design. Reidel, Dordrecht.zbMATHGoogle Scholar
  55. Plackett, R. L. and Burman, J. P. (1946). The design of optimum multifao toriai experiments. Biometrika 33, 305–325.MathSciNetzbMATHCrossRefGoogle Scholar
  56. Potthoff, R. F. and Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika 51, 313–326.MathSciNetzbMATHGoogle Scholar
  57. Pukelsheim, F. (1980). On linear regression designs which maxmize information. Journal of Statistical Planning and Inference 4, 339–364.MathSciNetzbMATHCrossRefGoogle Scholar
  58. Pukelsheim, F. (1993). Optimal design of experiments. Wiley, New York.zbMATHGoogle Scholar
  59. Puntanen, S. and Styan, G. P. H. (1989). The equality of the ordinary least squares estimator and the best linear unbiased estimator. The American Statistician 43(3), 153–163.MathSciNetGoogle Scholar
  60. Rao, C. R. (1959). Some problems involving linear hypotheses in multivariate analysis. Biometrika 46, 49–58.MathSciNetzbMATHGoogle Scholar
  61. Rao, C. R. (1965). The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. Biometrika 52, 447–458.MathSciNetzbMATHGoogle Scholar
  62. Rao, C. R. (1967). Least squares theory using an estimated dispersion matrix and its application to measurement of signals. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 1, 355–372.Google Scholar
  63. Rao, C. R. (1973). Some combinatorial problems of arrays and applications to experimental designs. In A Survey of Combinatorial Theory. Eds. J. N. Srivastava, F. Harray, C. R.Rao, G. C. Rota and S. S. Shrikhande. North-Holland, Amsterdam, 349–359.Google Scholar
  64. Schwabe, R. (1996). Optimum designs for multi-factor models. Lecture Notes in Statistics 113. Springer, New York.Google Scholar
  65. Searle, S. (1971). Linear models. Wiley, New York.zbMATHGoogle Scholar
  66. Searle, S. (1987). Linear models for unbalanced data. Wiley, New York.Google Scholar
  67. Searle, S. R., Casella, G. and McCulloch, C. E. (1992). Variance components. Wiley, New York.zbMATHCrossRefGoogle Scholar
  68. Shah, K. R. and Sinha, Bikas K. (1989). Theory of optimal designs. Lecture Notes in Statistics 54. Springer, New York.Google Scholar
  69. Silvey, S. D. (1978). Optimal design measures with singular information matrices. Biometrika 65, 553–559.MathSciNetzbMATHCrossRefGoogle Scholar
  70. Silvey, S. D. (1980). Optimum design. Chapman&Hall, London.CrossRefGoogle Scholar
  71. Sinha, Bikas K. (1970). On the Optimality of some designs. Calcutta Statistical Association Bulletin 19, 1–22.MathSciNetzbMATHGoogle Scholar
  72. Smith, K. (1918). On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper chcice of the distribution of observations. Biometrika 12, 1–85Google Scholar
  73. Swamy, P. A. V. B. (1971). Statistical inference in random coefficient re-gression models. Lecture Notes in Operational Research and Mathematical Systems 55. Springer, New York.Google Scholar
  74. Wynn, H. P. (1972). Results in the theory and construction of D-optimum experimental designs. Journal of the Royal Statistical Society Series B 34, 133–147.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Erkki P. Liski
    • 2
  • Nripes K. Mandal
    • 1
  • Kirti R. Shah
    • 4
  • Bikas K. Sinha
    • 3
  1. 1.Department of StatisticsCalcutta UniversityCalcuttaIndia
  2. 2.Department of Mathematics, Statistics, and PhilosophyUniversity of TampereTampereFinland
  3. 3.Stat-Math DivisonIndian Statistical InstituteCalcuttaIndia
  4. 4.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations