In this paper, a novel graphical method to classify spatial point patterns is proposed. This method is called the AG-curve. It is constructed using the results of hierarchical cluster analysis, and it has many variations corresponding to the various agglomeration methods used in such analysis. The characteristics of the AGsi-curve,which is a variant of the AG-curve, are clarified and several applications to real data are shown. The classification performance of the AGsi-curve is compared with that of other graphical methods, and the difference between the AGsi-curve and the other methods is shown graphically.

We proposed a modified non-overlapping template matching test and a method for specifying a pattern that appears too many times, in Takeda et al. (2014). The method that we proposed was effective for the most part, but had some difficulties. Our new contribution in this paper is to propose an improved method of identifying a pattern that appears too many times, in the non-overlapping template matching test for resolving these difficulties and to show how this identification test works effectively by some simulation studies.

In this study, we propose a new estimation procedure for incomplete survival data caused by nonignorable nonresponses or missing censoring indicators. It is widely known that if there is any nonignorable missingness or censoring indicators cannot be fully observed, the results from survival analysis such as the Kaplan-Meier estimator or the Cox proportional hazard model may be biased. However, it sometimes occurs that nonignorable missingness cannot be specified and that the censoring indicators are never or partially observed. We propose a Bayesian generalized method of moments (GMM) approach that utilizes population-level information to identify true survival time and estimates parameters. We apply the proposed model to analyze purchase duration in marketing using purchase history data.

Methods of estimating an unconstrained covariance matrix are derived using future data as well as current data in the likelihood. The estimators are obtained by optimizing coefficient(s) for adjusting the usual maximum likelihood estimators based on current data. The optimization is given by maximizing the expected log-likelihood over the distributions of future and current data. Under the Wishart and normal distributions,the coefficients in their adjusted estimators are obtained using known quantities. When a covariance matrix is structured with structural parameters, asymptotic adjustments of the Wishart maximum likelihood estimators are obtained. Similar estimators of an unconstrained covariance matrix derived by minimizing the mean square error are also given. Numerical illustrations with simulations are shown using factor analysis models. Methods of overcoming the problem of the dependence of the optimal values on unknown population values are discussed.

In regression analysis, stochastic models are often constructed to model relationships between outcomes and explanatory variables. We derive statistical interpretation about the underlying structure of data based on these models. When we use a linear regression model and the model provides good fitting to the data, it is straightforward to interpret the relation. However, there are cases where it may be difficult to formulate a linear model reflecting actual characteristics in detail. In such cases, a tree-structured approach is recommended, such as classification and regression trees (CART), which develops a tree and provides an interpretation of the data based on the fundamental model derived from the tree. Random Forest (RF) involves an ensemble learning method based on the trees and can predict outcomes more precisely. However,RF cannot provide a tree-structured model for interpreting the data. We examine a nonnegative garrote (NNG), a shrinkage estimator, and propose Garrote Trees (GT) as an adjustment of RF based on NNG. In addition, GT can lead making trees that are useful for interpretation of data. Two case studies of diabetes and prostate cancer data illustrate predictive accuracy and descriptive features of GT. Finally, our simulation studies show that the proposed method is highly accurate predictively and provides a potential ability to interpret the data from new meaningful standpoints.