The historical development of robust statistics

Original by E. Ronchetti, 2006, 4 pages 

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Research on the history of statistics and the different mathematicians that contributed to it

  • Robust statistic should be  included more naturally in the undergraduate and graduate programs
  • Classical statistics and econometrics are based on parametric models
  • Many classical statistics and econometric procedures are well-known for not being robust, because their results may depend crucially on the exact stochastic assumptions and on properties of a few observations in the sample
  • The results obtained by classical procedures can be misleading on real data applications
  • The theory of robust statistics deals with deviations from the assumptions on the model and is concerned with the construction of classical procedures which are still reliable and reasonably efficient in a neighborhood of the model

Main contributions of robust statistics

Fundamental papers : Tureky(1960), Huber (1964), Hampel (1968)

  • Models are only approximations to reality (Turkey 2960)
  • Multiple analyses and solutions of data-analysis problem (multiple tools at eneeded) (Turkey 1962)
  • The minimax approach (Huber 1964)
  • Stability measures functions (Hampel 1968,1974)
  • M-estimators (Huber 1964)
  • The breaking point (Hampel 198, 1971)  which is a measure of global stability for a statistical function

Example of financial models

  • One would like that the choice of a model used to price and hedge a financial instrument is driven by the features of the majority of the observed data rather than by a single data point or some historical period
  • Re-analysis of the empirical evidence of CKLS (one factor models) demonstrated how a robust analysis can provide insight
  • Found that there is a clustering of influential observations on the 1970-1982 sub period, well known to coincide with a temporary change in the monetary policy of the federal reserve