Modern Mathematical Statistics with Applications pp 331-381 | Cite as

# Point Estimation

Chapter

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## Abstract

Given a parameter of interest, such as a population mean *μ* or population proportion p, the objective of point estimation is to use a sample to compute a number that represents in some sense a good guess for the true value of the parameter. The resulting number is called a point estimate. In Section 7.1, we present some general concepts of point estimation. In Section 7.2, we describe and illustrate two important methods for obtaining point estimates: the method of moments and the method of maximum likelihood.

## Bibliography

- DeGroot, Morris, and Mark Schervish,
*Probability and Statistics*(3rd ed.), Addison-Wesley, Boston, MA, 2002. Includes an excellent discussion of both general properties and methods of point estimation; of particular interest are examples showing how general principles and methods can yield unsatisfactory estimators in particular situations.Google Scholar - Efron, Bradley, and Robert Tibshirani,
*An Introduction to the Bootstrap*, Chapman and Hall, New York, 1993. The bible of the bootstrap.CrossRefGoogle Scholar - Hoaglin, David, Frederick Mosteller, and John Tukey,
*Understanding Robust and Exploratory Data Analysis*, Wiley, New York, 1983. Contains several good chapters on robust point estimation, including one on*M*-estimation.Google Scholar - Hogg, Robert, Allen Craig, and Joseph McKean,
*Introduction to Mathematical Statistics*(6th ed.), Prentice Hall, Englewood Cliffs, NJ, 2005. A good discussion of unbiasedness.Google Scholar - Larsen, Richard, and Morris Marx,
*Introduction to Mathematical Statistics*(4th ed.), Prentice Hall, Englewood Cliffs, NJ, 2005. A very good discussion of point estimation from a slightly more mathematical perspective than the present text.Google Scholar - Rice, John,
*Mathematical Statistics and Data Analysis*(3rd ed.), Duxbury Press, Belmont, CA, 2007. A nice blending of statistical theory and data.Google Scholar

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