Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Bilinear Regression Analysis

Part of the book series: Lecture Notes in Statistics ((LNS,volume 220))

  • 1516 Accesses

Abstract

A short introduction to bilinear regression analysis is presented. The statistical paradigm is introduced. Moreover, bilinear regression models are presented together with a number of examples. Some historical remarks on the material of the book are given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aitken, A. C. (1935). Note on selection from a multivariate normal population. Proceedings of the Edinburgh Mathematical Society, Series 2, 4, 106–110.

    Article  MATH  Google Scholar 

  • Aitken, A. C. (1936). On least squares and linear combinations of observations. Proceedings of the Royal Society of Edinburgh, Section A, 55, 42–48.

    Article  MATH  Google Scholar 

  • Aitken, A. C. (1949). On the Wishart distribution in Statistics. Biometrika, 36, 59–62.

    Article  MathSciNet  MATH  Google Scholar 

  • Aldrich, J. (1999). Determinacy in the linear model: Gauss to Bose and Koopmans. International Statistical Review, 67, 211–219.

    Article  MATH  Google Scholar 

  • Anderson, T. W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics, 22, 327–351.

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson, T. W. (1958). An introduction to multivariate statistical analysis. New York/London: Wiley/Chapman & Hall.

    Google Scholar 

  • Anderson, T. W. (1984). An introduction to multivariate statistical analysis (2nd ed.). New York: Wiley.

    Google Scholar 

  • Anderson, T. W. (1996). R.A. Fisher and multivariate analysis. Statistical Science, 11, 20–34.

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson, T. W. (2003). An introduction to multivariate statistical analysis. Wiley series in probability and statistics (3rd ed.). Hoboken: Wiley-Interscience.

    Google Scholar 

  • Anderson, T. W. (2007). Multiple discoveries: Distribution of roots of determinantal equations. The Journal of Statistical Planning and Inference, 137, 3240–3248.

    Article  MathSciNet  MATH  Google Scholar 

  • Andersson, S. A., Marden, J. I., & Perlman, M. D. (1993). Totally ordered multivariate linear models. Sankhy \(\bar {a}\) , Series A, 55, 370–394.

    Google Scholar 

  • Andersson, S. A., & Perlman, M. D. (1993). Lattice models for conditional independence in a multivariate normal distribution. The Annals of Statistics, 21, 1318–1358.

    Google Scholar 

  • Andersson, S. A., & Perlman, M. D. (1998). Normal linear regression models with recursive graphical Markov structure. Journal of Multivariate Analysis, 66, 133–187.

    Google Scholar 

  • Bartholomew, D., Knott, M., & Moustaki, I. (2011). Latent variable models and factor analysis. A unified approach. Wiley series in probability and statistics (3rd ed.). Chichester: Wiley.

    Google Scholar 

  • Bartlett, M. S. (1934a). On the theory of statistical regression. Proceedings of the Royal Society of Edinburgh, 53, 260–283.

    Article  Google Scholar 

  • Bartlett, M. S. (1934b). The vector representation of a sample. Mathematical Proceedings of the Cambridge Philosophical Society, 30, 327–340.

    Article  MATH  Google Scholar 

  • Bartlett, M. S. (1939). A note on tests of significance in multivariate analysis. Mathematical Proceedings of the Cambridge Philosophical Society, 35, 180–185.

    Article  MATH  Google Scholar 

  • Bartlett, M. S. (1974). Historical remarks and recollections on multivariate analysis. Sankhy \(\bar {a}\) , Series B, 36, 107–114.

    Google Scholar 

  • Berger, J. O., & Molina, G. (2004). Some recent developments in Bayesian variable selection. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP Conference Proceedings (Vol. 735, pp. 417–428). Melville: American Institute of Physics.

    Google Scholar 

  • Bilodeau, M., & Brenner, D. (1999). Theory of multivariate statistics. Springer texts in statistics. New York: Springer.

    Google Scholar 

  • Bose, R. C. (1936). On the exact distribution of D2-statistic. Sankhy \(\bar {a}\) , 2, 143–154.

    Google Scholar 

  • Bose, R. C., & Roy, S. N. (1938). The distribution of the studentized D2-statistic. Sankhy \(\bar {a}\) , 4, 19–38.

    Google Scholar 

  • Box, G. E. P. (1950). Problems in the analysis of growth and wear curves. Biometrics, 6, 362–389.

    Article  Google Scholar 

  • Bravais, A. (1846). Analyse mathématique sur les probabilités des erreurs de situation d’un point. Mémoires de l’Institute de France, IX, 255–332 (in French).

    Google Scholar 

  • Bulmer, M. (2003). Francis Galton: Pioneer of heredity and biometry. Baltimore: Johns Hopkins University Press.

    Google Scholar 

  • Burnaby, T. P. (1966). Growth invariant discriminant functions and generalized distances. Biometrics, 22, 96–110.

    Article  MathSciNet  MATH  Google Scholar 

  • Cochran, W. G. (1934). The distribution of quadratic forms in a normal system, with applications to the analysis of covariance. Mathematical Proceedings of the Cambridge Philosophical Society, 30, 178–191.

    Article  MATH  Google Scholar 

  • Cowles, M. (2001). Statistics in psychology: An historical perspective (2nd ed.). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Cox, D. R. (2006). Principles of statistical inference. Cambridge: Cambridge University Press.

    Google Scholar 

  • Cox, D. R., & Wermuth, N. (1996). Multivariate dependencies. Models, analysis and interpretation. Monographs on statistics and applied probability (Vol. 67). London: Chapman & Hall.

    Google Scholar 

  • David, H. A. (2006). The introduction of matrix algebra into statistics. The American Statistician, 60, 162.

    Article  MathSciNet  Google Scholar 

  • Davison, A. C. (2003). Statistical models. Cambridge series in statistical and probabilistic mathematics (Vol. 11). Cambridge: Cambridge University Press.

    Google Scholar 

  • Dempster, A. P. (1969). Elements of continuous multivariate analysis. New York: Addison-Wesley.

    Google Scholar 

  • Dillon, W. R., & Goldstein, M. (1984). Multivariate analysis: Methods and applications. New York: Wiley.

    Google Scholar 

  • Drton, M., & Richardson, T. S. (2004). Multimodality of the likelihood in the bivariate seemingly unrelated regressions model. Biometrika, 91, 383–392.

    Google Scholar 

  • Druilhet, P. (1999). Optimality of neighbour balanced designs. The Journal of Statistical Planning and Inference, 81, 141–152.

    Article  MathSciNet  MATH  Google Scholar 

  • Drygas, H. (1970). The coordinate-free approach to Gauss-Markov estimation. Lecture notes in operations research and mathematical systems (Vol. 40). New York: Springer.

    Google Scholar 

  • Eaton, M. L. (1983). Multivariate statistics. A vector space approach. New York: Wiley.

    Google Scholar 

  • Edgeworth, F. Y. (1892). Correlated averages. Philosophical Magazine (5th Series), 34, 190–204.

    Google Scholar 

  • Evans, M. J., Fraser, D. A. S., & Monette, G. (1986). On principles and arguments to likelihood. With discussion and a rejoinder by the authors. The Canadian Journal of Statistics, 14, 181–199.

    Google Scholar 

  • Everitt, B. S., Landau, S., Leese, M., & Stahl, D. (2011). Cluster analysis. Wiley series in probability and statistics (5th ed.). Chichester: Wiley.

    Google Scholar 

  • Farebrother, R. W. (1999). Fitting linear relationships: A history of the calculus of observations 1750–1900. New York: Springer.

    Book  MATH  Google Scholar 

  • Fearn, T. (1975). A Bayesian approach to growth curves. Biometrika, 62, 89–100.

    Article  MathSciNet  MATH  Google Scholar 

  • Filipiak, K., & Markiewicz, A. (2017). Universally optimal designs under interference models with and without block effects. Communications in Statistics: Theory and Methods, 46, 1127–1143.

    Google Scholar 

  • Filipiak, K., & von Rosen, D. (2012). On MLEs in an extended multivariate linear growth curve model. Metrika, 75, 1069–1092.

    Google Scholar 

  • Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10, 507–521.

    Google Scholar 

  • Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179–188.

    Article  Google Scholar 

  • Fisher, R. A. (1938). The statistical utilization of multiple measurements. Annals of Eugenics, 8, 376–386.

    Article  MATH  Google Scholar 

  • Fisher, R. A. (1939). The sampling distribution of some statistics obtained from non-linear equations. Annals of Eugenics, 9, 238–249.

    Article  MathSciNet  Google Scholar 

  • Fujikoshi, Y., Enomoto, R., & Sakurai, T. (2013). High-dimensional AIC in the growth curve model. Journal of Multivariate Analysis, 122, 239–250.

    Google Scholar 

  • Fujikoshi, Y., Kanda, T., & Ohtaki, M. (1999). Growth curve model with hierarchical within-individuals design matrices. Annals of the Institute of Statistical Mathematics, 51, 707–721.

    Google Scholar 

  • Fujikoshi, Y, Ulyanov, V. V., & Shimizu, R. (2010). Multivariate statistics. High-dimensional and large-sample approximations. Wiley series in probability and statistics. Hoboken: Wiley.

    Google Scholar 

  • Gabriel, K. R. (1998). Generalised bilinear regression. Biometrika, 85, 689–700.

    Article  MathSciNet  MATH  Google Scholar 

  • Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.

    Article  Google Scholar 

  • Galton, F. (1888). Co-relations and their measurement, chiefly from anthropometric data. Proceedings of the Royal Society of London, 45, 135–145.

    Google Scholar 

  • Galton, F. (1889). Natural inheritance. London: Macmillan.

    Google Scholar 

  • Geiser, C., Keller, B. T., & Lockhart, G. (2013). First- versus second-order latent growth curve models: Some insights from latent state-trait theory. Structural Equation Modeling, 20, 479–503.

    Google Scholar 

  • Geisser, S. (1980). Growth curve analysis. In P. R. Krishnaiah (Ed.), Handbook of statistics (Vol. 1, pp. 89–115). New York: North-Holland.

    Google Scholar 

  • Geisser, S. (2006). Modes of parametric statistical inference. With the assistance of Wesley Johnson. With a foreword by Anne Flaxman Geisser. Wiley series in probability and statistics. Hoboken: Wiley-Interscience.

    Google Scholar 

  • Girshick, M. A. (1939). On the sampling theory of roots of determinantal equations. Annals of Mathematical Statistics, 10, 203–224.

    Article  MathSciNet  MATH  Google Scholar 

  • Gleser, L. J., & Olkin, I. (1970). Linear models in multivariate analysis. In Essays in probability and statistics (pp. 267–292). Chapel Hill: University of North Carolina Press.

    Google Scholar 

  • Gram, J. P. (1879). Om ræckkeudviklinger, bestemte ved hjælp af de mindste kvadraters methode. Dissertation, Høst og Søn, København (in Danish).

    Google Scholar 

  • Greenacre, M. J. (1984). Theory and applications of correspondence analysis. London: Academic.

    Google Scholar 

  • Grizzle, J. E., & Allen, D. M. (1969). Analysis of growth and dose response curves. Biometrics, 25, 357–381.

    Google Scholar 

  • Hald, A. (1981). T.N. Thiele’s contributions to statistics. International Statistical Review, 49, 1–20.

    Google Scholar 

  • Hald, A. (2002). On the history of series expansions of frequency functions and sampling distributions, 1873–1944. Matematisk-fysiske meddelelser, 49. ISSN: 00233323.

    Google Scholar 

  • Herr, D. G. (1980). On the history of the use of geometry in the general linear model. The American Statistician, 34, 43–47.

    MathSciNet  MATH  Google Scholar 

  • Hoff, P. (2015). Multilinear tensor regression for longitudinal relational data. Annals of Applied Statistics, 9, 1169–1193.

    Article  MathSciNet  MATH  Google Scholar 

  • Hotelling, H. (1931). The generalization of Student’s ratio. Annals of Mathematical Statistics, 2, 170–198.

    Article  MATH  Google Scholar 

  • Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. The Journal of Educational Psychology, 24, 417–441, 498–520.

    Article  MATH  Google Scholar 

  • Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28, 321–377.

    Article  MATH  Google Scholar 

  • Hsu, P. L. (1939). On the distribution of roots of certain determinantal equations. Annals of Eugenics, 9, 250–258.

    Article  MathSciNet  Google Scholar 

  • Hyvärinen, A., Karhunen, J., & Oja, E. (2001). Independent component analysis. New York: Wiley.

    Google Scholar 

  • Imori, S., & von Rosen, D. (2015). Covariance components selection in high-dimensional growth curve model with random coefficients. Journal of Multivariate Analysis, 136, 86–94.

    Google Scholar 

  • Irwin, J. O. (1934). On the independence of the constituent items in the analysis of variance. Journal of the Royal Statistical Society Supplements, 1, 236–251.

    Article  MATH  Google Scholar 

  • Jensen, S. T. (1988). Covariance hypotheses which are linear in both the covariance and the inverse covariance. The Annals of Statistics, 16, 302–322.

    Article  MathSciNet  MATH  Google Scholar 

  • Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). New York: Springer.

    Google Scholar 

  • Kanda, T. (1994). Growth curve model with covariance structures. Hiroshima Mathematical Journal, 24, 135–176.

    Article  MathSciNet  MATH  Google Scholar 

  • Kariya, T. (1985). Testing in the multivariate general linear model. New York: Kinokuniya.

    Google Scholar 

  • Kariya, T., & Kurata, H. (2004). Generalized least squares. Chichester: Wiley.

    Google Scholar 

  • Kariya, T., & Sinha, B. K. (1989). Robustness of statistical tests. Statistical modeling and decision science. Boston: Academic.

    Google Scholar 

  • Kempthorne, O. (1952). The design and analysis of experiments. New York/London: Wiley/Chapman & Hall.

    Google Scholar 

  • Kendall, M. G. (1957). A course in multivariate analysis. Griffin’s statistical monographs & courses (Vol. 2). New York: Hafner Publishing Company.

    Google Scholar 

  • Khatri, C. G. (1966). A note on a MANOVA model applied to problems in growth curves. Annals of the Institute of Statistical Mathematics, 18, 75–86.

    Article  MathSciNet  MATH  Google Scholar 

  • Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer (in German).

    Google Scholar 

  • Kolodziejczyk, S. (1935). On an important class of statistical hypotheses. Biometrika, 27, 161–190.

    Article  MATH  Google Scholar 

  • Kotz, S., Balakrishnan, N., & Johnson, N. L. (2000). Continuous multivariate distributions, 1. Models and applications. Wiley series in probability and statistics: Applied probability and statistics (2nd ed.). New York: Wiley.

    Google Scholar 

  • Kshirsagar, A. M., & Smith, W. B. (1995). Growth curves. New York: Marcel Dekker.

    Google Scholar 

  • Kunert, J., & Martin, R. J. (2000). On the determination of optimal designs for an interference model. The Annals of Statistics, 28, 1728–1742.

    Google Scholar 

  • Lauritzen, S. L. (1996). Graphical models. Oxford statistical science series (Vol. 17). New York/Oxford: The Clarendon Press/Oxford University Press.

    Google Scholar 

  • Letac, G., & Massam, H. (2008). The noncentral Wishart as an exponential family, and its moments. Journal of Multivariate Analysis, 99, 1393–1417.

    Google Scholar 

  • Linder, M., & Sundberg, R. (2002). Precision of prediction in second-order calibration, with focus on bilinear regression methods. Journal of Chemometrics, 16, 12–27.

    Google Scholar 

  • Madow, W. G. (1938). Contributions to the theory of multivariate statistical analysis. Transactions of the American Mathematical Society, 44, 454–490.

    Article  MathSciNet  MATH  Google Scholar 

  • Mahalanobis, P. C. (1930). On tests and measures of group divergence. Part I. Theoretical formulae. Journal of the Asiatic Society of Bengal, 26, 541–588.

    Google Scholar 

  • Mahalanobis, P. C. (1936). On the generalised distance in statistics. Proceedings of National Institute of Sciences (India), 2, 49–55.

    Google Scholar 

  • Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate analysis. Probability and mathematical statistics: A series of monographs and textbooks. New York: Academic.

    Google Scholar 

  • Mayo, D. G., & Cox, D. R. (2006). Frequentist statistics as a theory of inductive inference. In 2nd Lehmann Symposium—Optimality. IMS Lecture Notes—Monograph Series (Vol. 49, pp. 77–97). Beachwood: Institute of Mathematical Statistics.

    Google Scholar 

  • McLachlan, G. J. (1992). Discriminant analysis and statistical pattern recognition. Wiley series in probability and mathematical statistics: Applied probability and statistics. New York: Wiley.

    Google Scholar 

  • Monhor, D. (2012). A very short note on the origins of correlated bivariate normal distribution with particular relevance to earth sciences. Acta Geodaetica et Geophysica Hungarica, 47, 117–122.

    Article  MathSciNet  Google Scholar 

  • Morrison, D. F. (2005). Multivariate statistical methods. McGraw-Hill series in probability and statistics (4th ed.). Belmont: Thomson/Brooks/Cole.

    Google Scholar 

  • Muirhead, R. J. (1982). Aspects of multivariate statistical theory. New York: Wiley.

    Google Scholar 

  • Nayak, T. P. (2009). Impact of Karl Pearson’s work on statistical developments in India. International Statistical Review, 77, 72–80.

    Article  Google Scholar 

  • Olkin, I., & Shrikhande, S. S. (1954). On a modified T2 problem. Annals of Mathematical Statistics, 25, 808 (abstract).

    Google Scholar 

  • Pan, J.-X., & Fang, K. T. (2002). Growth curve models and statistical diagnostics. New York: Springer.

    Google Scholar 

  • Pearson, K. (1896). Mathematical contributions to the theory of evolution. III. Regression, heredity and panmixia. Philosophical Transactions of the Royal Society A, 187, 253–318.

    Article  Google Scholar 

  • Pearson, K. (1901). On lines and planes of closest fit to systems of points in space. Philosophical Magazine (6th series), 2, 559–572.

    Google Scholar 

  • Perlman, M. D. (1987). Group symmetry covariance models. (Discussion of “A Review of Multivariate Analysis” by Mark Schervish.) Statistical Science, 2, 421–425.

    Article  Google Scholar 

  • Potthoff, R. F., & Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51, 313–326.

    Google Scholar 

  • Rao, C. R. (1948). Tests of significance in multivariate analysis. Biometrika, 35, 58–79.

    Article  MathSciNet  MATH  Google Scholar 

  • Rao, C. R. (1958). Some statistical methods for comparison of growth curves. Biometrics, 14, 1–17.

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Rao, C. R. (1966a). Discriminant function between composite hypotheses and related problems. Biometrika, 53, 339–345.

    Article  MathSciNet  MATH  Google Scholar 

  • Rao, C. R. (1966b). Covariance adjustment and related problems in multivariate analysis. In P. R. Krishnaiah (Ed.), Multivariate analysis, (pp. 87–103). New York: Academic.

    Google Scholar 

  • Rao, C. R. (1967). Least squares theory using an estimated dispersion matrix and its application to measurement of signals. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, Berkeley, 1965/1966 (pp. 355–372). Berkeley: University of California Press.

    Google Scholar 

  • Rao, C. R., & Kleffe, J. (1988). Estimation of variance components and applications. North-Holland series in statistics and probability (Vol. 3), Amsterdam: North-Holland.

    Google Scholar 

  • Rencher, A. C., & Christensen, W. F. (2012). Methods of multivariate analysis. Wiley series in probability and statistics (3rd ed.). Hoboken: Wiley.

    Google Scholar 

  • Roy, S. N. (1939). p-Statistics or some generalisations in analysis of variance appropriate to multivariate problems. Sankhy \(\bar {a}\) , 4, 381–396.

    Google Scholar 

  • Roy, S. N. (1957) Some aspects of multivariate analysis. New York/Calcutta: Wiley/Indian Statistical Institute.

    Google Scholar 

  • Schafer, G., & Vovk, V. (2006). The sources of Kolmogorov’s Grundbegriffe. Statistical Science, 21, 70–98.

    Google Scholar 

  • Schervish, M. J. (1987). A review of multivariate analysis. With discussion and a reply by the author. Statistical Science, 2, 396–433.

    Article  MathSciNet  MATH  Google Scholar 

  • Seal, H. L. (1967). Studies in the history of probability and statistics. XV: The historical development of the Gauss linear model. Biometrika, 54, 1–24.

    Article  MathSciNet  MATH  Google Scholar 

  • Searle, S. R. (2000). The infusion of matrices into statistics. IMAGE, 24, 25–32.

    Google Scholar 

  • Searle, S. R. (2005). Recollections from a 50-year random walk midst matrices, statistics and computing. In P. S. P. Cowpertwait (Ed.), Proceedings of the 14th workshop on matrices and statistics. Research letters in the information and mathematical sciences (Vol. 8, pp. 45–52). Palmerston North: Massey University.

    Google Scholar 

  • Seber, G. A. F. (1984). Multivariate observations. Wiley series in probability and mathematical statistics: Probability and mathematical statistics. New York: Wiley.

    Google Scholar 

  • Seely, J. (1971). Quadratic subspaces and completeness. Annals of Mathematical Statistics, 42, 710–721.

    Article  MathSciNet  MATH  Google Scholar 

  • Shao, J. (2003). Mathematical statistics. Springer texts in statistics (2nd ed.). New York: Springer.

    Google Scholar 

  • Siotani, M., Hayakawa, T., & Fujikoshi, Y. (1985). Modern multivariate statistical analysis: A graduate course and handbook. American sciences press series in mathematical and management sciences (Vol. 9). Columbus: American Sciences Press.

    Google Scholar 

  • Srivastava, M. S., & Carter, E. M. (1983). An introduction to applied multivariate statistics. New York: North-Holland.

    Google Scholar 

  • Srivastava, M. S., & Khatri, C. G. (1979). An introduction to multivariate statistics. New York: North-Holland.

    Google Scholar 

  • Srivastava, M. S., & von Rosen, D. (1999). Growth curve models. In Multivariate analysis, design of experiments, and survey sampling. Statistics: A series of textbooks and monographs (Vol. 159, pp. 547–578). New York: Dekker.

    Google Scholar 

  • Stigler, S. M. (1986). The history of statistics: The quantification of uncertainty before 1900. Cambridge: Harvard University Press.

    Google Scholar 

  • Stigler, S. M. (2012). Karl Pearson and the rule of three. Biometrika, 99, 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  • Stone, M. (1977). A unified approach to coordinate-free multivariate analysis. Annals of the Institute of Statistical Mathematics, 29, 43–57.

    Article  MathSciNet  MATH  Google Scholar 

  • Stone, M. (1987). Coordinate-free multivariable statistics. An illustrated geometric progression from Halmos to Gauss and Bayes. Oxford statistical science series (Vol. 2). New York: The Clarendon Press/Oxford University Press.

    Google Scholar 

  • Student. (1908). The probable error of a mean. Biometrika, 6, 1–25.

    Google Scholar 

  • Takeuchi, K., Yanai, H., & Mukherjee, B. N. (1982). The foundations of multivariate analysis. A unified approach by means of projection onto linear subspaces. New York: A Halsted Press Book/Wiley.

    Google Scholar 

  • Thiele, T. N. (1889). Forelæsninger over almindelig iagttagelseslære: Sandsynlighedsregning og mindste kvadraters methode (in Danish). København: Reitzel.

    Google Scholar 

  • Timm, N. H. (1997). The CGMANOVA model. Communications in Statistics: Theory and Methods, 26, 1083–1098.

    Article  MathSciNet  MATH  Google Scholar 

  • Tocher, K. D. (1952). On the concurrence of a set of regression lines. Biometrika, 39, 109–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Valderrama, P., & Poppi, R. J. (2008). Bilinear least squares (BLLS) and molecular fluorescence in the quantification of the propranolol enantiomers. Analytica Chimica Acta, 623, 38–45.

    Google Scholar 

  • Verbeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. Springer series in statistics. New York: Springer.

    Google Scholar 

  • Verbyla, A. P., & Venables, W. N. (1988). An extension of the growth curve model. Biometrika, 75, 129–138.

    Google Scholar 

  • von Bortkiewicz, Dr. L. (1917). Die Iterationen. Ein Beitrag zur Wahrscheinlichkeitstheorie. Berlin: Julius Springer (in German).

    Google Scholar 

  • von Rosen, D. (1989). Maximum likelihood estimators in multivariate linear normal models. Journal of Multivariate Analysis, 31, 187–200.

    Article  MathSciNet  MATH  Google Scholar 

  • von Rosen, D. (1991). The growth curve model: A review. Communications in Statistics: Theory and Methods, 20, 2791–2822.

    Article  MathSciNet  MATH  Google Scholar 

  • Votaw, D. F. (1948). Testing compound symmetry in a normal multivariate distribution. Annals of Mathematical Statistics, 19, 447–473.

    Article  MathSciNet  MATH  Google Scholar 

  • Whittaker, J. (1990). Graphical models in applied multivariate statistics. Wiley series in probability and mathematical statistics: Probability and mathematical statistics. Chichester: Wiley.

    Google Scholar 

  • Wichura, M. J. (2006). The coordinate-free approach to linear models. Cambridge series in statistical and probabilistic mathematics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Wilks, S. S. (1932). Certain generalizations in the analysis of variance. Biometrika, 24, 471–494.

    Article  MATH  Google Scholar 

  • Wilks, S. S. (1946). Sample criteria for testing equality of means, equality of variances, and equality of covariances in a normal multivariate distribution. Annals of Mathematical Statistics, 17, 257–281.

    Article  MathSciNet  MATH  Google Scholar 

  • Wishart, J. (1928). The generalised product moment distribution in samples from a normal multivariate population. Biometrika, 20 A, 32–52.

    Article  MATH  Google Scholar 

  • Wishart, J. (1938). Growth-rate determinations in nutrition studies with the bacon pig, and their analysis. Biometrika, 30, 16–28.

    Article  Google Scholar 

  • Withers, C. S., & Nadarajah, S. (2012). Moments and cumulants for the complex Wishart. Journal of Multivariate Analysis, 112, 242–247.

    Article  MathSciNet  MATH  Google Scholar 

  • Woolson, R. F., & Leeper, J. D. (1980). Growth curve analysis of complete and incomplete longitudinal data. Communications in Statistics: Theory and Methods, 9, 1491–1513.

    Article  MathSciNet  MATH  Google Scholar 

  • Yates, F. (1933). The analysis of replicated experiments when the field results are incomplete. Empire Journal of Experimental Agriculture, 1, 129–142.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden

    Dietrich von Rosen

Authors
  1. Dietrich von Rosen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

von Rosen, D. (2018). Introduction. In: Bilinear Regression Analysis. Lecture Notes in Statistics, vol 220. Springer, Cham. https://doi.org/10.1007/978-3-319-78784-8_1

Download citation

Publish with us

Policies and ethics

Search

Navigation