Recently some visual analyses of multivariate data have been studied in the field of statistical graphics. Several dynamic graphical methods have been proposed. Moving or rotating the graphical data points continuously, we can explore the latent structure of the data interactively. One of these methods, Linked Lines Rotation Graphics (LLRG) has been discussed by Wakimoto(1993). In this paper, we propose a visual method for finding clusters of multivariate data with LLRG. Numerical examples of the proposed method are shown.
keywords: Statistical graphics, Dynamic graphical method, Clustering method}
Missing values are almost unavoidable in many practical data analyses.
Particularly in the analysis of experimental data, since the number of
observations is generally not so large, the influence of missing should
be carefully checked. This paper discusses several graphical methods
which are useful in assessing the effect of missing values in the
analysis of variance of randomized block design.
Some techniques such as simple imputation and multiple imputation have
been proposed in the literature to cope with the missing values.
However, with the use of recent computer facilities, more effective
methods which utilize graphical representation seem to be called for.
Techniques considered in this paper are functional representations of
F-ratios and P-values against imputed values and graphical
representations of the result of Monte Carlo simulation as an
approximation to the Bayesian posterior distribution of missing value.
Numerical examples are shown to illustrate the techniques.
It is also claimed that the present methods can be used not only to
assess the effect of missing values but also to evaluate the
sensitiveness of obtained data.
An experiment was carried out to investigate the utility of graphical methods such as face graph, radar chart and letter graph for classifying multivariate data. To do this 3, 5 and 7 dimensional observations were generated based on models $N(\mu_{k},I)$ of three groups, i.e., k=1, 2 and 3, where the distances among the groups were set as 3, 4 and 5 regardless of their dimensions. For each kind of graph 40 subjects were asked to classify 30 observations from 3 groups, which were expressed in a graph, into 3 groups, and correct/incorrect numbers of classification were counted. In face graph and radar chart, the rate of correct classification was the best in the case of 5 variables while the rate was the best in the case of 3 variables in letter graph. These facts suggest that the rate of correct classification decreased as the number of variables increase over a fixed number. It was also shown that the human's ability of classification was inferior to a numerical method such as principal component analysis.
keywords: Face graph, Radar chart, Letter graph, Cluster analysis
A backward elimination procedure is proposed for variable selection in
principal component analysis. In this procedure a variable is discarded
among the existing variables in each step in such a way that it causes the
smallest effect on the configuration of the principal component (PC) scores.
The RV-coefficient (Robert \& Escoufier, 1976) is used to evaluate the
difference of the configurations of the PC scores and the perturbation
theory of eigenvalue problems as well as the exact method are utilized to
compute the effect on the configurations.
A set of real data and four sets of artificial data were analyzed for the
comparison of our method with other methods proposed so far. In these
numerical examples our method made reasonable results of variable selection
in principal component analysis.
In this paper, we propose and discuss three kinds of approximate
confidence intervals for Coefficient of Variation (CV), the classical
confidence interval based on Normal approximation, the confidence
intervals based on second-order and third-order Cornish-Fisher
expansions. All the intervals are based on the jackknife-t quantity, a jackknife
bias-adjusted random variable studentized by its jackknife estimate
of standard deviation. Within a practical range of CV, in terms of
coverage probability, the approximate confidence interval based on
third-order Cornish-Fisher expansion of the jackknife-t quantity
improves the one based on second-order Cornish-Fisher expansion,
which in turn improves the one based on basic Normal approximation. Our numerical experiment is carried out by assuming the original
basic random variable being Normal.
Approximations for the distribution function of the jackknife-t
quantity are also discussed. The conclusion is similar to the case of confidence interval estimation: the third-order Edgeworth
approximation is better than its second-order counterpart, which
behaves better
than Normal approximation, provided that the true coefficient of
variation is reasonably stable (not too large).
Many types of data sets are daily statistically analyzed
to make clear the physical phenomena by researchers.
However, there exist many biased or misapplied
results which are misleading.
It depends on the lack of statistical sensibility.
Therefore, the system of statistical education, that is,
(1)statistics literacy, (2)school education of statistics, (3)general
education of statistics and (4)specialized education of statistics,
are needed to be regularly constructed.
In this paper, we discuss the problems of statistical education
from the point of view of 5W1H + 1W, that is, ``when, where, who, what,
how, why and whom''.
Then, there are some problems to be improved on
the number of statistical researchers and teaching materials
and so on.
As an example of the systematic specialized education of statistics,
the statistical curriculum of a new department in
Okayama University is offered.
We also demonstrate a new approach to statistical software
for learning statistics to comprehend the properties of
statistical methods, based on histogram matrix.
Current methods of random number generation and Monte-Carlo method contain various problems awaiting solutions. The author's personal views about these points will be stated. Lastly, some important problems waiting for solutions will be mentioned.
keywords: Arithmetic random generator, Physical random generator, Pertubation, Quantum Mechanics