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Parameter Estimation

  • Bernard Flury
Part of the Springer Texts in Statistics book series (STS)

Abstract

Estimation of parameters is a central topic in statistics. In probability theory we study the distribution of random variables, assuming they follow certain distributions, and try to find out what is likely to happen and what is unlikely. Conversely, in statistics we observe data and try to find out which distribution generated the data. In the words of my colleague R.B. Fisher: “In probability, God gives us the parameters and we figure out what is going to happen. In statistics, things have already happened, and we are trying to figure out how God set the parameters.”

Keywords

Mean Square Error Likelihood Function Maximum Likelihood Estimator Bootstrap Sample Wing Length 
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.

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Suggested Further Reading

  1. Casella, G., and Berger, R.L. 1990. Statistical Inference. Belmont, CA: Duxbury Press.zbMATHGoogle Scholar
  2. Silvey, S.D. 1975. Statistical Inference. London: Chapman and Hall.zbMATHGoogle Scholar
  3. Diaconis, P., and Efron, B. 1983. Computer-intensive methods in statistics. Scientific American 248 (May), 116–130.CrossRefGoogle Scholar
  4. Efron, B. 1982. The Jackknife, the Bootstrap, and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
  5. Efron, B., and Gong, G. 1983. A leisurely look at the bootstrap, the jackknife, and other resampling plans. The American Statistician 37, 36–48.MathSciNetGoogle Scholar
  6. Efron, B., and Tibshirani, R. 1993. An Introduction to the Bootstrap. London: Chapman and Hall.zbMATHGoogle Scholar
  7. Edwards, A.W.F. 1984 Likelihood Cambridge University Press CambridgezbMATHGoogle Scholar
  8. Kalbfleisch, J.G. 1985 Probability and Statistical Inference 2 Springer New YorkGoogle Scholar
  9. Watson, G.S. 1964. A note on maximum likelihood. Sankhya A 26, 303–304.zbMATHGoogle Scholar
  10. Dempster, A.P., Laird, N.M., and Rubin, D.B. 1977. Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society Series B, 39, 1–38.MathSciNetzbMATHGoogle Scholar
  11. Little, R.J.A., and Rubin, D.B. 1987. Statistical Analysis with Missing Data. New York: Wiley.zbMATHGoogle Scholar
  12. McLachlan, G.J., and Krishnan, T. 1997. The EM Algorithm and Extensions. New York: Wiley.zbMATHGoogle Scholar
  13. Rubin, D.B., and Szatrowski, T.H. 1982. Finding maximum likelihood estimates of patterned covariance matrices by the EM algorithm. Biometrika 69, 657–660.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Bernard Flury
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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