Construction of simultaneous confidence intervals for multinomial
proportions is one of the most important statistical procedures in many
real-life applications, such as statistical quality control, survey
sampling, opinion polls, *etc.* Basically,
there are two popular forms of simultaneous confidence intervals for
*m*-dimension multinomial proportions.
The first one is the conventional confidence
intervals (CCI) which have lengths proportionate to the estimated standard
error of sample proportions. Therefore, the length of each interval
depends on how much the corresponding sample proportion deviates from
0.5, longer interval for less deviation and shorter interval for more
deviation. Gold (1963), Cochran (1963), Quesenberry and Hurst (1964),
Goodman (1965), Tortora (1978), Bailey (1980), Kwong and Iglewicz (1996),
focused on the construction of CCI.
The second one is called quick simultaneous confidence intervals
(QSCI) which have same length for all the intervals.
Angers (1974), Thompson(1987), Fitzpatrick and Scott (1987),
Sison and Glaz (1995), Kwong (1998) discussed the
procedures for the construction of QSCI. A brief comparison between
the two forms of confidence intervals can be found in Fitzpatrick and
Scott (1987).

After incorporating the singular correlation structure
based on Kwong's Inequalities into the
evaluation of the critical values for the construction of QSCI, Kwong (1998)
improved the performance of QSCI. However, the approach works only for
as the computational time increases rapidly for large *m*.
With the application of the new approach
of evaluating singular multivariate normal distribution
described in Section 2.2, we can
construct QSCI (see Kwong (1998) for details) for any *m*. Analogous to
the case of construction of QSCI, we
modify the existing approaches for constructing CCI
after taking the singular correlation structure of sample proportions into
consideration. Besides, we extend the results to the construction of
all pairwise simultaneous confidence intervals for multinomial
proportions in the forms of CCI and QSCI.

- Confidence Intervals for Multinomial Proportions
- Pairwise Confidence Intervals for Multinomial Proportions

2001-02-09