csetMV function

Confidence regions and intervals for a normal mean and variance

Computes boundaries of (simultaneous) confidence regions for the mean and variance of a normal distribution using different methods.

csetMV(dat, n, method, alpha=0.1, scale="var", steps=500)

Arguments

• dat: A vector of numeric values assumed to follow a normal distribution. Not required for method="cheng.iles" or "min.area".
• n: A numeric value giving the sample size. Only required for method="cheng.iles" or "min.area".
• method: A character string specifying the method to be used. See details for available methods.
• alpha: A numeric value giving the type I error level to be controlled. Default is 0.1.
• scale: A character string specifying whether the variance (var) or standard deviation (sd) is to be plotted on the y axis. Not required for method="cheng.iles" or "min.area".
• steps: An integer setting the initial number of steps for the search algorithm. Default is 800.

Details

Available methods are: mood for the classical region described in Mood (1950); large for the large-sample approximation region described in section 4.1 of Arnold & Shavelle (1998); plugin for a plug-in variant of the large-sample approximation region described in section 4.2 of Arnold & Shavelle (1998); pluginF for the plug-in variant of the large-sample approximation region described in section 4.3 of Arnold & Shavelle (1998) using an asymptotic F distribution as in Douglas (1993); lrt for the likelihood ratio test region described in section 4.4 of Arnold & Shavelle (1998); cheng.iles for the region described in Cheng & Iles (1983); min.area for the minimum-area region described in Frey et al. (2009).

Returns

An object of class JOCMV.

References

Barry C. Arnold & Robert M. Shaville (1998) Joint confidence sets for the mean and variance of a normal distribution. The American Statistician, 52(2), 133--140.

R. C. H. Cheng & T. C. Iles (1983) Confidence bands for cumulative distribution functions of continuous random variables. Technometrics, 25(1), 77--86.

J. B. Douglas (1993) Confidence regions for parameter pairs. The American Statistician, 47(1), 43--45.

Jesse Frey, Osvaldo Marrero, Douglas Norton (2009) Minimum-area confidence sets for a normal distribution. Journal of Statistical Planning and Inference, 139(3), 1023--1032.

Alexander M. Mood (1950) Introduction to the Theory of Statistics. McGraw-Hill, New York, NY.

Author(s)

Philip Pallmann (p.pallmann@lancaster.ac.uk )

Note

Warning: please use with care! Some of the functionality has not yet been thoroughly tested.

See Also

cset for (simultaneous) confidence regions and intervals around multivariate normal means.

Examples

## Not run:

# Simultaneous 90% confidence regions for the mean and variance or sd of univariate normal data

univar <- rnorm(n=50)

moodvar <- csetMV(dat=univar, method="mood", alpha=0.1, scale="var")
summary(moodvar)
plot(moodvar)

moodsd <- csetMV(dat=univar, method="mood", alpha=0.1, scale="sd")
summary(moodsd)
plot(moodsd)
## End(Not run)