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19 - Estimation algorithms

from Part IV - Statistical inference

Published online by Cambridge University Press:  05 June 2012

Hisashi Kobayashi
Affiliation:
Princeton University, New Jersey
Brian L. Mark
Affiliation:
George Mason University, Virginia
William Turin
Affiliation:
AT&T Bell Laboratories, New Jersey
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Summary

In this chapter we will study statistical methods to estimate parameters and procedures to test the goodness of fit of a model to the experimental data. We are primarily concerned with computational algorithms for these methods and procedures. The expectation-maximization (EM) algorithm for maximum-likelihood estimation is discussed in detail.

Classical numerical methods for estimation

As we stated earlier, it is often the case that a maximum-likelihood estimate (MLE) cannot be found analytically. Thus, numerical methods for computing the MLE are important. Finding the maximum of a likelihood function is an optimization problem. There are a number of optimization algorithms and software packages. In this and the next sections we will discuss several important methods that are pertinent to maximization of a likelihood function: the method of moments, the minimum χ2method, the minimum Kullback–Leibler divergence method, and the Newton–Raphson algorithm. In Section 19.2 we give a full account of the EM algorithm, because of its rather recent development and its increasing applications in signal processing and other science and engineering fields.

Method of moments

This method is typically used to estimate unknown parameters of a distribution function by equating the sample mean, sample variance, and other higher moments calculated from data to the corresponding moments expressed in the parameters of interest.

Type
Chapter
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Probability, Random Processes, and Statistical Analysis
Applications to Communications, Signal Processing, Queueing Theory and Mathematical Finance
, pp. 554 - 570
Publisher: Cambridge University Press
Print publication year: 2011

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  • Estimation algorithms
  • Hisashi Kobayashi, Princeton University, New Jersey, Brian L. Mark, George Mason University, Virginia, William Turin, AT&T Bell Laboratories, New Jersey
  • Book: Probability, Random Processes, and Statistical Analysis
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977770.020
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  • Estimation algorithms
  • Hisashi Kobayashi, Princeton University, New Jersey, Brian L. Mark, George Mason University, Virginia, William Turin, AT&T Bell Laboratories, New Jersey
  • Book: Probability, Random Processes, and Statistical Analysis
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977770.020
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Estimation algorithms
  • Hisashi Kobayashi, Princeton University, New Jersey, Brian L. Mark, George Mason University, Virginia, William Turin, AT&T Bell Laboratories, New Jersey
  • Book: Probability, Random Processes, and Statistical Analysis
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511977770.020
Available formats
×