Projection pursuit is a computer-intensive method for statistical analysis which intends to clarify property of multivariate data by projecting them onto a lower-dimensional subspace.
In practice, the projection pursuit is performed based on an algorithm to find a lower-dimensional subspace by maximizing an objective function called projection index which is a measure of interestingness of the projected data.
In this paper, we try to evaluate how the direction of projection determined in the process of the projection pursuit is affected by perturbation of the data points.
This paper presents a method for fitting the quadratic curve which has the least-squares distance from two variable data. Fitting of smooth curves is one of the most important themes in pattern recognition and data analysis. Simple, multiple or multivariate regression analyses are in use for a data set consists of observations on some variables which can be classified into response and explanatory ones. But, there are few analyses that work well for a data set whose variables can not be distinguished between response and explanatory.
For such data set, a straight line, which has least sum of square distances from data points, is obtained by using principal component analysis. We extend the principal component analysis to the fitting of quadratic curve and show performance of the proposed method by a numerical example.
Hazard models that link covariates to hazard function of survival distribution are roughly classified into multiplicative and additive ones. The well-known proportional hazard model used widely in survival study, is a special one of the multiplicative models. In this paper, we examine the adequacy to evaluate the effect of covariates on survival time by means of the multiplicative models (or especially, the proportional hazard modeD , based on the fitting of a comprehensive model, i.e. data adaptive hazard model, which includes additive and multiplicative models as special cases. Further, we examine the goodness of fit of a model, i.e. generalized additive proportional hazard model which extends linear predictor into additive one, in order to diagnose the adequacy of the proportional hazard model within the frame of the multiplicative models. Comparing the results from the fittings of the generalized additive and the proportional hazard models, we evaluate the adequacy to express the effect of covariates on survival by the proportional hazard model utilizing a few practical examples.
As a result, it is seen that the data adaptive model is useful to diagnose the goodness of fit of the multiplicative models, especially the proportional hazard model. It is also seen that the fitting of the generalized additive proportional hazard model is useful to examine "linearity" assumption in the proportional hazard model.
Multiple comparison procedures have commonly been used to compare several sample means in the area of applied statistics. Though such a procedure generally repeats many tests, it is often difficult to interpret the results of the procedures and to derive unified conclusion. We discuss sample mean clustering methods as substitutes of the multiple comparison procedures. In particular we deal with the six clustering methods discussed in Tasaki et al.(1987) and a mixture model approach in McLachlan & Basford (1988) . For the hierarchical methods of these it is useful to summarize their results in dendrograms. We propose a modified method to represent dendrograms that is suitable for comparing sample means, and a graphical method to represent the goodness of fit of the mixture model. Then we compare the performance of the seven clustering methods and their associated graphical ones through reanalyses of three sets of data from published literature .
keywords: Analysis of variance, Graphical representation, Sample mean clustering, Dendrogram, Mixture model, Half circle graph