A knowledge discovery method is useful to describe the data structure
using some rules, defined by the functional relationship among variables,
in exploratory data analysis.
In this paper, two knowledge discovery softwares, IDIS and Datalogic/R,
were applied to clinical data on circulatory disease and
structure activity relationship data on antiviral agent for investigating
the efficiency and the performance of these methods.
As a result, we found that the rules, induced by the methods, were efficient to
describe the structure of the data. By changing the condition (parameters) of
the methods, we can get several number of rules and knowledges which imply the
flexible interpretations. This will be impotant point for exploratory data analysis.
We report some topics on spline smoothing, that is, a method of nonparametric regression.
First we describe one-dimensional spline smoothing.
An estimator of the regression function is derived, and the methods of computing estimates and choosing the smoothing parameter are summarized.
Next, in the case of several explanatory variables, we discuss a semiparametric regression model.
In this model, a nonparametric function on one (or more) variable(s),
and a linear function on the other variables, are fitted,
and we assume the additivity on them.
The estimators of both components are derived, and additionally
this model is applied to some data of agricultural experiment.
In the latter part we describe some asymptotic properties
on semiparametric regression estimators.
Rice (1986) pointed out that estimates of the regression coefficients
in the parametric part were biased.
In order to reduce the bias, two estimators were proposed.
So we try to compare numerically by simulation
to what extent the bias of these estimators is reduced.
As a result, we find that the partial regression estimator has the effect
of reducing the bias to some extent even if sample size is small,
whereas the two-stage spline smoothing estimator is effective
only if sample size is small.
The power transformation proposed by Box & Cox(1964) does not generally have scale-invariance with the transformation of observations. For this reason, it is meaningless to perform subsequent statistical processing by the quantities or statistics which depend on scale of observations in before and after of the power transformation. Then, in order to take away the scaling effect which depends on the power transforming parameter, it may be recommended to apply ``the normalizing power transformation'' which adjusted the ordinary transformation formula by n root of Jacobian of the transformation. In this paper, some properties of the normalizing power transformation were evaluated by investigating mainly distribution of observations, particularly behavior of mean, variance, and relative change rate of them with respect to adjustment of scale-invariance. Further, we examined the relative performance of the normalizing power transformation to ordinary one through some examples cited from published literatures and simulation. The results suggest that the normali zing power transformations take away the scaling effect which depends on the power transforming parameter.
keywords: Ordinary power transformation, Normalizing power transformation, Jacobian of transformation, Relative change rateThe gross period which indicates the length between two neighboring maxima (or minima) for a sequence can be stochastically derived as a function of turning value r for an infinite discrete random number sequence. The mean gross period can be expressed by 3+3/(2r-1). The present theory directly provides a systematic and effective method which tests the uniformity and non-regularity of the pseudo random numbers.
keyword: Gross period, Random number sequence, Discrete random numbers
The quantitative document analysis which originated from the
idea of mathematician, Augustus de Morgan, in 1851 has been
developed in this century. This new method of document analysis
attracts much attention in the humanities because
of recent widespread availability of computers and associated software.
In this paper, at first we review the history of quantitative
document analysis briefly. Then, we discuss the problems and
potential of quantitative analysis for documents, especially
for Japanese documents.