Wavelet transform is a well-known and remarkable way of
time--frequency analysis and it is used in various fields. Although
an important problem in wavelet transform is how to select mother
wavelet, the unified selection of mother wavelet is not yet realized
at present.
In this paper, we classify a mother wavelet into the complex type and
the real type. The real type component is further divided into a
symmetric type, an skew-symmetric type and an asymmetric type by
the symmetric property of the function. The properties of so
classified mother wavelets are examined by a reference
signal. The selection and applicability of each mother wavelet are
also examined, and it is found that the complex type mother wavelet is
most efficient for time--frequency analysis.
Group sequential procedure is to test sequentially the hypothesis of
difference between two treatments based on group observations in
clinical trials when the response is the normal variable.
In some clinical trials, it is more preferable that we deal with $p$
responses at a time rather than only one response to evaluate the
effect of a treatment.
In order to carry out the group sequential test based on multivariate
observations, we can consider to use $\chi^{2}$ statistic or
Hotelling's T2 statistic.
However the statistics have a quadratic form, we can not directly
examine the contribution of some responses in $p$ responses.
We assume in this study that the $p$ response vector on each of two
treatments has a multivariate normal distribution, then we can derive
the group sequential procedures which test the existence of the
contribution of some responses in $p$ responses based on the
difference of two population mean vectors.
For incorporating the group sequential test, we propose a group
sequential T2 statistic by applying T2 statistic discussed in
Rao's additional information test (1952).
Furthermore, we propose another modified group sequential T2
statistic by extending Jennison and Turnbull's method (1991)
in order to realize the group sequential test where the average
sample size is reduced.
After the repeated confidence boundaries are decided by each of the
two group sequential T2 statistics, we will compare two group
sequential procedures based on two T2 statistics regarding the
average sample size and the power of the test.
In this paper, we propose a new measure of space distortion,
which has been introduced by Lance & Williams (1967), in combinatorial
cluster analysis.
In particular, our measure is defined for
each clustering process, not only for the clustering method.
This means that the measure depends both on the method and
on the data.
Since the space distortion is measured as a numerical value,
it makes easy to select the method in the actual application.
Furthermore, a new combinatorial clustering method which can
control the space distortion is proposed by using our measure.
The validity of the new methods is discussed by analyzing the
numerical example.
Data mining has been successful because of the users' needs to
get useful knowledge from large database in computers and the
tremendous progress of computing power.
Although the era of trial use is over and users are getting good
results, it is still hard to figure the whole picture of data mining
because of the wide range of its applications.
This paper covers the current status of data mining mainly in the
viewpoint of business application.
In this paper, at first we point out the importance of overall process
of data mining to get useful knowledge from vast amount of data.
Then we review some techniques of common use, and overview the
difference between statistical analysis and data mining.
We also refer to some guidelines for selecting software packages,
some application cases, challenges for data mining and future
directions.