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A confidence band is an object used in a statistical analysis, and most usually occurs as part of a graphical presentation of results. Confidence bands are closely allied in concept to confidence intervals, but the interpretation is subtly different.## References

One application where confidence bands are used is in regression analysis, in the case of a simple regression involving a single dependent variable. Results can be presented in the form of a plot showing the estimated regression line. A first extension of this is to include lines showing point-wise confidence limits: the lines are drawn through the upper and lower limits obtained treating each possible value of the dependent variable separately. Two cases are commonly dealt with:

- confidence limits for the location of "true" regression line;
- confidence limits for the value of a new observation from the same population as the experimental data.

A second extension of the plot is to include confidence bands: these are lines derived from the observed dataset which define a region such that, across notional repetitions of the experiment, regions devised in the same way have a given probability that the true regression line lies entirely within such a region.

A confidence band typically has a similar shape to the region defined by the limits of the point-wise confidence intervals, but is rather wider.

A second type of application where confidence bands are available are those deriving from the empirical distribution function. Again, simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a confidence band for the distribution function as a whole. See Setting confidence limits for a distribution function for example, or Owen (1995).

Confidence bands have also been devised for applications to spectral density estimation.

- Liu W., Lin S., Piegorsch W.W.. (2008) "Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model". International Statistical Review, 76 (1), 39–57 doi:10.1111/j.1751-5823.2007.00027.x
- Owen A.B. (1995) "Nonparametric likelihood confidence bands for a distribution function". Journal of the American Statistical Association, 90, 516–521.
- Neumann, M.H., Paparoditis, E. (2008) "Simultaneous confidence bands in spectral density estimation". Biometrika, 95 (2). doi:10.1093/biomet/asn005

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Last updated on Thursday May 29, 2008 at 07:43:14 PDT (GMT -0700)

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Last updated on Thursday May 29, 2008 at 07:43:14 PDT (GMT -0700)

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