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Statistical Inference

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Epistemic Processes
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Abstract

A summary of statistical inference theory as it has been developed up to now, is given. Both frequentist and Bayesian inference are covered. The recent concept of confidence distributions is described. As a preparation for the next chapter, statistical inference is also seen as a special case of inference in a general epistemic process.

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References

  • Bernardo, J. M., & Smith, A. F. M. (1994). Bayesian theory. Chichester: Wiley.

    Book  Google Scholar 

  • Bickel, P. J., & Doksum, K. A. (2001). Mathematical statistics. Basic ideas and selected topics (2nd ed.). New Jersey: Prentice Hall.

    MATH  Google Scholar 

  • Box, G. E. P., & Tiao, G. C. (1973). Bayesian inference in statistical analysis. New York: Wiley.

    MATH  Google Scholar 

  • Breiman, L. (2001). Statistical modeling: The two cultures. Statistical Science, 16, 199–231.

    Article  MathSciNet  Google Scholar 

  • Casella, G., & Berger, R. L. (1990). Statistical inference. Pacific Grove, CA: Wadsworth and Brooks.

    MATH  Google Scholar 

  • Cochran, W. G. (1977). Sampling techniques (3rd ed.). New York: Wiley.

    MATH  Google Scholar 

  • Congdon, P. (2006). Bayesian statistical modelling (2nd ed.). Chichester: Wiley.

    Book  Google Scholar 

  • Cook, R. D., Li, B., & Chiaromonte, F. (2010). Envelope models for parsimonious and efficient multivariate linear regression. Statistica Sinica, 20, 927–1010.

    MathSciNet  MATH  Google Scholar 

  • Cook, R. D., Helland, I. S., & Su, Z. (2013). Envelopes and partial least squares regression. Journal of the Royal Statistical Society, Series B, 75, 851–877.

    Article  MathSciNet  Google Scholar 

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

    Book  Google Scholar 

  • Cox, D. R., & Donnelly, C. A. (2011). Principles of applied statistics. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Efron, B. (1998). R.A. Fisher in the 21st century. Statistical Science, 13, 95–122.

    Article  MathSciNet  Google Scholar 

  • Efron, B. (2015). Frequency accuracy of Bayesian estimates. Journal of the Royal Statistical Society, B, 77, 617–646.

    Article  Google Scholar 

  • Gelman, A., & Robert, C. P. (2013). “Not only defended but also applied”: The perceived absurdity of Bayesian inference. The American Statistician, 67, 1–5.

    Article  MathSciNet  Google Scholar 

  • Helland, I. S. (2004). Statistical inference under symmetry. International Statistical Review, 72, 409–422.

    Article  Google Scholar 

  • Helland, I. S. (2010). Steps towards a unified basis for scientific models and methods. Singapore: World Scientific.

    MATH  Google Scholar 

  • Helland, I. S., Sæbø, S., & Tjelmeland, H. (2012). Near optimal prediction from relevant components. Scandinavian Journal of Statistics, 39, 695–713.

    Article  MathSciNet  Google Scholar 

  • Helland, I. S., Sæbø, S., Almøy, T., & Rimal, R. (2018). Model and estimators for partial least squares regression. Journal of Chemometrics. https://doi.org/10.1002/cem.3044.

  • Hermansen, G., Cunen, C., & Stoltenberg, E. A. (2017). Ny bok: Confidence, likelihood, probability. statistical inference with confidence distributions. (In Norwegian). Tilfeldig Gang, 34 no. 1.

    Google Scholar 

  • Kass, R. E., & Wasserman, L. (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91, 1343–1370.

    Article  Google Scholar 

  • LeCam, L. (1990). Maximum likelihood: An introduction. International Statistical Review, 58, 153–171.

    Article  Google Scholar 

  • Lehmann, E. L. (1999). Elements of large-sample theory. New York: Springer.

    Book  Google Scholar 

  • Lehmann, E. L., & Casella, G. (1998). Theory of point estimation. New York: Springer.

    MATH  Google Scholar 

  • McCullagh, P. (2002). What is a statistical model? Annals of Statistics, 30, 1225–1310.

    Article  MathSciNet  Google Scholar 

  • Schweder, T., & Hjort, N. L. (2002). Confidence and likelihood. Scandinavian Journal of Statistics, 29, 309–332.

    Article  MathSciNet  Google Scholar 

  • Schweder, T., & Hjort, N. L. (2016). Confidence, likelihood, probability. Statistical inference with confidence distributions. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Sen, P. K., & Singer, J. M. (1993). Large sample methods in statistics. London: Chapman and Hall, Inc.

    Book  Google Scholar 

  • Sæbø, S., Almøy, T., & Helland, I. S. (2015). Simrel - a versatile tool for linear model data simulation based on the concept of a relevant subspace and relevant predictors. Chemometrics and Intelligent Laboratory Systems, 146, 128–135.

    Article  Google Scholar 

  • Xie, M., & Singh, K. (2013). Confidence distributions, the frequentist distribution estimator of a parameter - a review. Including discussion. International Statistical Review, 81, 1–77.

    Article  Google Scholar 

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Helland, I.S. (2018). Statistical Inference. In: Epistemic Processes. Springer, Cham. https://doi.org/10.1007/978-3-319-95068-6_2

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