Abstract
Between 1936 and 1940 Fisher published four articles on statistical discriminant analysis, in the first of which [CP 138] he described and applied the linear discriminant function. Prior to Fisher the main emphasis of research in this, area was on measures of difference between populations based on multiple measurements. In this presentation, I shall briefly summarize the early work from Karl Pearson up to Mahalanobis, and then describe the major contributions associated with Fisher. These include the derivation of the linear discriminant function and its relationship to regression in the two-sample case, extensions to s populations for s 003E 2, and a test of significance associated with the linear discriminant function.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References and Bibliography
Early Period
Pearson, K. (1916). “On the Probability that Two Independent Distributions of Frequency Are Really from the Same Population,” Biometrika, 8, 250–254.
Tildesley, M.L. (1921). “A First Study of the Burmese Skull,” Biometrika, 13, 247–251.
Pearson, K. (1926). “On the Coefficient of Racial Likeness,” Biometrika, 18, 105–117.
Morant, G.M. (1926). “A First Study of Craniology of England and Scotland from Neolithic to Early Historic Times, with Special Reference to Anglo-Saxon Skulls in London Museums,” Biometrika, 18, 56–98.
Mahalanobis, P.C. (1927). “Analysis of Race Mixture in Bengal,” Journal and Proceedings of the Asiatic Society of Bengal, 23, 301–333.
Mahalanobis, P.C. (1928). “A Statistical Study of the Chinese Head,” Man in India, 8, 107–122.
Morant, G.M. (1928). “A Preliminary Classification of European Races Based on Cranial Measurements,” Biometrika, 20, 301–375.
Pearson, K. (1928). “The Application of the Coefficient of Racial Likeness to Test the Character of Samples,” Biometrika, 20, 294–300.
Romanovsky, V. (1928). “On the Criteria that Two Given Samples Belong to the Same Normal Population,” Metron, 7, 3–46.
Mahalanobis, P.C. (1930). “On Tests and Measures of Group Divergence,” Journal and Proceedings of the Asiatic Society of Bengal, 26, 541–588.
Hotelling, H. (1931). “The Generalization of Student’s Ratio,” The Annals of Mathematical Statistics, 2, 360–378.
Woo, T.L. and Morant, G.M. (1932). “A Preliminary Classification of Asiatic Races Based on Cranial Measurements,” Biometrika, 24, 108–134.
Pearson, E.S. and Wilks, S.S. (1933). “Methods of Statistical Analysis Appropriate for Samples of Two Variables,” Biometrika, 25, 353–378.
Meyer, H.A. and Deming, W.E. (1935). “On the Influence of Classification on the Determination of a Measurable Characteristic,” Journal of the American Statistical Association, 30, 671–677.
Mahalanobis, P.C. (1936). “On the Generalized Distance in Statistics,” Proceedings of the National Institute of Sciences of India, 2, 49–55..
Contemporaries of Fisher
Barnard, M.M. (. 1935 ). “The Secular Variations of Skull Characters in Four Series of Egyptian Skulls,” Annals of Eugenics, 6, 352–371.
Bose, S.N. (1936). “On the Complete Moment Coefficients of the D2 Statistic”, Sankhya, 2, 385–396.
Bose, R.C. (1936). “On the Exact Distribution and Moment Coefficients of the D2- Statistic,” Sankhya, 2, 143–154. Corrected and modified paper: Sankhya, 2, 379–384.
Martin, E.S. (1936). “A Study of the Egyptian Series of Mandibles with Special Reference to Mathematical Methods of Sexing,” Biometrika., 28, 149–178.
Smith, H.F. (1936). “A Discriminant Function for Plant Selection,” Annals of Eugenics, 7, 240–250.
Bose, S.N. (1937). “On the Moment-Coefficients of the D2-Statistic, and Certain Integral and Differential Equations Connected with the Multivariate Normal Populations,” Sankhya, 3, 105–124.
Bose, R.C. and Roy, S.N. (1937). “On the Distribution of Fisher’s Taxonomic Coefficient and Studentised D2-Statistic,” Science and Culture, 3, 335.
Bose, R.C. and Roy, S.N. (1938). “The Distribution of the Studentised D2-Statistic” Sankhya, 4, 19–38.
Hsu, P.L. (1938). “Notes on Hotellings Generalized T2,” The Annals of Mathematical Statistics, 9, 231–243.
Bartlett, M.S. (1939). “The Standard Errors of Discriminant Function Coefficients,” Supplement to the Journal of the Royal Statistical Society, 6, 169–173.
Girshick, M.A. (1939). “On the Sampling Theory of Roots of Determinantal Equations” The Annals of Mathematical Statistics, 10, 203–224.
Hsu, P.L. (1939). “On the Distribution of Roots of Certain Determinanta1 Equations” Annals of Eugenics, 9, 250–258.
Roy, S.N. (1939). “A Note on the Distribution of the Studentised D2-Statistic,” Sankhya, 4, 373–380.
Roy, S.N. (1939). “P-Statistics and Some Generalizations in Analysis of Variance,” Sankhya, 4, 381–396.
Welch, B.L. (1939). “Note on Discriminant Functions,” Biometrika, 31, 218–220.
Roy, S.N. and Bose, R.C. (1940). “The Use and Distribution of the Studentised D2-Statistic when the Variances and Covariances are Based on Samples,” Sankhya, 4, 535–542.
Bhattacharya, D.P. and Narayan, R.D. (1941). “Moments of the D2-Statistic for Populations with Unequal Dispersions,” Sankhya, 5, 401–412.
Goodwin, C.N. and Morant, G.M. (1941). “The Human Remains of Iron Age and Other Periods from Maiden Castle, Dorset,” Biometrika, 31, 295–312.
Wald, A. (1944). “On a Statistical Problem Arising in the Classification of an Individual into One of Two Groups,” The Annals of Mathematical Statistics, 15, 145–162.
Von Mises, R. (1954). “On the Classification of Observation Data into Distinct Groups,” The Annals of Mathematical Statistics, 16, 68–73.
Recent References
Cacoullos, T. and Styan, G.P.A. (1973). “A Bibliography of Discriminant Analysis,” in Discriminant Analysis and Applications edited by T. Cacoullos. New York: Academic Press.
Das Gupta, S. (1973). “Theories and Methods in Classification: A Review,” in Discriminant Analysis and Applications edited by T. Cacoullos. New York: Academic Press.
Rao, C.R. (1973). Linear Statistical Inference and Its Applications. 2nd edition. New York: John Wiley and Sons. [Discussion of discriminant analysis and classification in Chapter 8].
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Das Gupta, S. (1980). Discriminant Analysis. In: Fienberg, S.E., Hinkley, D.V. (eds) R.A. Fisher: An Appreciation. Lecture Notes in Statistics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6079-0_16
Download citation
DOI: https://doi.org/10.1007/978-1-4612-6079-0_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90476-4
Online ISBN: 978-1-4612-6079-0
eBook Packages: Springer Book Archive