Discriminant Analysis

  • Wolfgang Karl HärdleEmail author
  • Léopold Simar


Discriminant analysis is used in situations where the clusters are known a priori. The aim of discriminant analysis is to classify an observation, or several observations, into these known groups. For instance, in credit scoring, a bank knows from past experience that there are good customers (who repay their loan without any problems) and bad customers (who showed difficulties in repaying their loan). When a new customer asks for a loan, the bank has to decide whether or not to give the loan. The past records of the bank provides two data sets: multivariate observations \(x_i\) on the two categories of customers (including, for example, age, salary, marital status, the amount of the loan, etc.). The new customer is a new observation x with the same variables. The discrimination rule has to classify the customer into one of the two existing groups and the discriminant analysis should evaluate the risk of a possible “bad decision”.


  1. R.A. Johnson, D.W. Wichern, Applied Multivariate Analysis, 4th edn. (Prentice Hall, Englewood Cliffs, New Jersey, 1998)zbMATHGoogle Scholar
  2. P.A. Lachenbruch, M.R. Mickey, Estimation of error rates in discriminant analysis. Technometrics 10, 1–11 (1968)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ladislaus von Bortkiewicz Chair of StatisticsHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institute of Statistics, Biostatistics and Actuarial SciencesUniversité Catholique de LouvainLouvain-la-NeuveBelgium

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