Bulletin of the Computational Statistics of Japan

The new concept named "hyper volume" for statistical pattern recognition is discussed in this paper. In pattern recognision using this new concept, each pattern is considered as a "hyper volume", while in conventional approaches it is treated as a "point". The new classification method called "(flat) hyper sphere method" is developed based on this concept. This new method has useful properties which have never been obtained in ordinary classification methods. Combining fuzzy theory with this new classification method, the hyper sphere method is further developed to the "sloped hyper sphere method". In this paper, these two classification methods, which are newly developed, are discussed in comparison with an ordinary classification method, k-NN.

View full abstract

Three methods commonly used to estimate unknown parameters in the factor analysis model, i.e., simple least-squares (SLS), weighted least-squares (WLS), and normal maximum likelihood (NML) methods, are compared by a Monte Carlo study with respect to their performances and robustness to the lack of normality. Our experiment was conducted with 200 replications for every combination of levels of the following four conditions : method (3 levels), sample size (2 levels), uniqueness (2 levels) and choice of non-normal variable (2 levels). It was found that SLS performed most favorably for all non-normal distribution, when sample size was relatively small and/or unique variances were relatively large, and that WLS was most robust and NML and SLS were equally sensitive when the distribution had non-zero kurtosis or skewness. Moreover, it was found that the effect of the kurtosis of the non-normal distribution on the estimation error was more serious than one of the skewess of the non-normal distribution.

View full abstract

The latent class analysis was first developed as a method to formalate latent concept which dominates manifest behavior in the field of social science. In the ordinary latent class analysis the data of binary responses of all items are treated, and a group of subjects is divided into some latent classes. We propose a latent class analysis of the item selection data that are obtained when an answerer selects the definite number of items. We consider two types of selection style, permutation and combination of items. An estimation method of latent parameters is presented and numerical experiments are done.

View full abstract

Show abstractHide abstract

In fitting problem of statistical model, power-normal transformation intends to satisfy the assumptions of (i) additivity of the model, (ii) constant variance of error term, and (iii) normality of response observations, by transforming the scale of observations. In applying the power-normal transformation, we can think of two different approaches, i.e., one intends to achieve the linearlity or additivity of the assumed model after the transformation, and another to satisfy the normality of error term or to identify the distribution (on the original scale) before the transformation, namely, the power-normal distribution (PND). In this paper, we briefly explain PND, as a theoretical distribution which supports the underlying concept of the power-normal transformation, and its properties. Then, we evaluate asymptotic behavior of maximum likelihood estimators of three parameters of PND, namely transforming parameter (λ), and location (μ) and variability (σ) which have meaning as mean and standard deviation of truncated normal distribution with truncating point k, after the transformation. It was clearly shown as a result of the evaluation that, if k is large, the asymptotic variance and covariance of the maximum likelihood estimators μ^^^ of μ and σ^^^^2 of σ^2 are not influenced by k, and that the maximum likelihood estimator λ^^^ of λ only influence the asymptotic behavior of μ^^^ and σ^^^. In addition, we mention various problems related to the power-normal transformation, especially, those concerning to the interpretation of λ. We also suggest the general formulation for the class of standardized transformation that adjusts the scale-variance of the power-normal transformation.

View full abstract

Download PDF (1678K)

Register with J-STAGE for free!