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.
Bickel, P. J., & Doksum, K. A. (2001). Mathematical statistics. Basic ideas and selected topics (2nd ed.). New Jersey: Prentice Hall.
Box, G. E. P., & Tiao, G. C. (1973). Bayesian inference in statistical analysis. New York: Wiley.
Breiman, L. (2001). Statistical modeling: The two cultures. Statistical Science, 16, 199–231.
Casella, G., & Berger, R. L. (1990). Statistical inference. Pacific Grove, CA: Wadsworth and Brooks.
Cochran, W. G. (1977). Sampling techniques (3rd ed.). New York: Wiley.
Congdon, P. (2006). Bayesian statistical modelling (2nd ed.). Chichester: Wiley.
Cook, R. D., Li, B., & Chiaromonte, F. (2010). Envelope models for parsimonious and efficient multivariate linear regression. Statistica Sinica, 20, 927–1010.
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.
Cox, D. R. (2006). Principles of statistical inference. Cambridge: Cambridge University Press.
Cox, D. R., & Donnelly, C. A. (2011). Principles of applied statistics. Cambridge: Cambridge University Press.
Efron, B. (1998). R.A. Fisher in the 21st century. Statistical Science, 13, 95–122.
Efron, B. (2015). Frequency accuracy of Bayesian estimates. Journal of the Royal Statistical Society, B, 77, 617–646.
Gelman, A., & Robert, C. P. (2013). “Not only defended but also applied”: The perceived absurdity of Bayesian inference. The American Statistician, 67, 1–5.
Helland, I. S. (2004). Statistical inference under symmetry. International Statistical Review, 72, 409–422.
Helland, I. S. (2010). Steps towards a unified basis for scientific models and methods. Singapore: World Scientific.
Helland, I. S., Sæbø, S., & Tjelmeland, H. (2012). Near optimal prediction from relevant components. Scandinavian Journal of Statistics, 39, 695–713.
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.
Kass, R. E., & Wasserman, L. (1996). The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91, 1343–1370.
LeCam, L. (1990). Maximum likelihood: An introduction. International Statistical Review, 58, 153–171.
Lehmann, E. L. (1999). Elements of large-sample theory. New York: Springer.
Lehmann, E. L., & Casella, G. (1998). Theory of point estimation. New York: Springer.
McCullagh, P. (2002). What is a statistical model? Annals of Statistics, 30, 1225–1310.
Schweder, T., & Hjort, N. L. (2002). Confidence and likelihood. Scandinavian Journal of Statistics, 29, 309–332.
Schweder, T., & Hjort, N. L. (2016). Confidence, likelihood, probability. Statistical inference with confidence distributions. Cambridge: Cambridge University Press.
Sen, P. K., & Singer, J. M. (1993). Large sample methods in statistics. London: Chapman and Hall, Inc.
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.
Xie, M., & Singh, K. (2013). Confidence distributions, the frequentist distribution estimator of a parameter - a review. Including discussion. International Statistical Review, 81, 1–77.
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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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DOI: https://doi.org/10.1007/978-3-319-95068-6_2
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