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 riles, 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 nunber of rules and knowledge which imply the flexible interpretations. This will be inpotant point for exploratory data analysis.

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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 descrbe 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 that 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.

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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 pbservations in before and after of 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 evaliated 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 normalizing power transformations take away the scaling effect which depends on the power transformation parameter.

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The 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 systenmatic and effective method which tests the uniformity and non-regularity of the pseudo random numbers.

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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.

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[in Japanese]

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