Statistical theory

The theory of statistics includes a number of topics:

Statistical models of the sources of data and typical problem formulation:

1. Sampling from a finite population
2. Measuring observational error and refining procedures
3. Studying statistical relations

Generating informative data using optimization and randomization while measuring and controlling observational error: Optimization reduces the cost of data while meeting statistical needs, while randomization warrants reliable inferences:

1. Design of experiments to determine treatment effects
2. Survey sampling to describe natural populations

Summarizing statistical data in conventional forms (also known as descriptive statistics)

1. Choosing summary statistics to describe a sample
2. Fitting probability distributions to sample data

Interpreting statistical data is the final objective of all research:

1. Common assumptions that we make
2. Likelihood principle
3. Estimating parameters
4. Testing statistical hypotheses

According to the American Statistical Association, Deming, Sir Ronald Fisher, and CR Rao are statisticians who have had the greatest impact on statistical theory.^[1].

See also

• Mathematical statistics
• Probability
• Statistics
• List of statistical topics

Bibliography

• Peirce, C. S.
  • (1876), "Note on the Theory of the Economy of Research" in Coast Survey Report, pp. 197–201 (Appendix No. 14), NOAA PDF Eprint. Reprinted 1958 in Collected Papers of Charles Sanders Peirce 7, paragraphs 139–157 and in 1967 in Operations Research 15 (4): pp. 643–648, Abstract from JSTOR. . doi:10.1287/opre.15.4.643. 
  • (1877–1878), "Illustrations of the Logic of Science"
  • (1883), "A Theory of Probable Inference"
  • and Jastrow, Joseph (1885), "On Small Differences in Sensation" in Memoirs of the National Academy of Sciences 3: pp. 73–83. Eprint.

• Bickel, Peter J. and Doksum, Kjell A. (2001). Mathematical Statistics: Basic and Selected Topics. I (Second (updated printing 2007) ed.). Pearson Prentice-Hall. 
• Lehmann, Erich (1959). Testing Statistical Hypotheses. 
• Lehmann, Erich (1983). Theory of Point Estimation. 
• Liese, Friedrich and Miescke, Klaus-J. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer. 

• Hinkelmann, Klaus and Kempthorne, Oscar (2008). Design and Analysis of Experiments. I, II (Second ed.). Wiley. ISBN 978-0-470-38551-7. 
• Bailey, R. A (2008). Design of Comparative Experiments. Cambridge University Press. ISBN 978-0-521-68357-9.  Pre-publication chapters are available on-line.
• Atkinson, A. C. and Donev, A. N. and Tobias, R. D. (2007). Optimum Experimental Designs, with SAS. Oxford University Press. pp. 511+xvi. ISBN 978-0-19-929660-6. 

• Cochran, William G. (1977). Sampling Techniques (Third ed.). Wiley. ISBN 0-471-16240-X. 
• Särndal, Carl-Erik, Swensson, Bengt, and Wretman, Jan (1992). Model Assisted Survey Sampling. Springer-Verlag. ISBN 0-387-40620-4. 

• Freedman, David A. (2009). Statistical Models: Theory and Practice (Second ed.). Cambridge University Press. ISBN 9780521671057. 
• A.C. Davidson Statistical Models. Cambridge University Press (2003).

References