Mihoko Minami

Robust extraction of local structures by the minimum β-divergence method

This paper discusses a new highly robust learning algorithm for exploring local principal component analysis (PCA) structures in which an observed data follow one of several heterogeneous PCA models. The proposed method is formulated by minimizing beta-divergence. It searches a local PCA structure based on an initial location of the shifting parameter and a value for the tuning parameter beta. If the initial choice of the shifting parameter belongs to a data cluster, then the proposed method detects the local PCA structure of that data cluster, ignoring data in other clusters as outliers. We discuss the selection procedures for the tuning parameter beta and the initial value of the shifting parameter mu in this article. We demonstrate the performance of the proposed method by simulation. Finally, we compare the proposed method with a method based on a finite mixture model.

Anticipatory postural adjustments contribute to age-related changes in compensatory steps associated with unilateral perturbations

Compensatory steps are essential for preventing falls following perturbations. This study aimed to explore age-related changes in compensatory steps to unilateral perturbations, specifically in terms of whether anticipatory postural adjustments (APAs) play a role in stabilizing lateral balance. Five young and five elderly male adults participated. The split-belt treadmill was used to provide bi- and unilateral perturbations, as forward or backward transitions, applied 10 times in random order. Backward steps evoked by unilateral forward perturbations were evaluated. We measured temporal characteristics, mediolateral (ML) center of mass (COM) motion, and ML step length of compensatory steps. Compensatory steps to unexpected perturbations showed delayed onset of foot-off (FO) and expanded lateral swing length in elderly compared to young subjects. Differences in COM motions and step width arose related to APAs. Elderly subjects showing APAs exhibited no significant differences in ML COM, ML COM velocity, or ML swing length compared to young subjects. However, elderly subjects without APAs showed significant changes toward instability in these parameters. The fact that APAs play a notable role, particularly in the elderly, in stability offers a new insight into preventing falls. However, APAs occurred in 29% of the steps of young and 35% of the steps of elderly subjects. If the occurrence of APAs in elderly people in response to compensatory steps was more frequent, fall risk would be reduced. Further studies, particularly into APA frequency, might contribute to improved intervention to prevent falls.

Estimation of similarity measure for multivariate normal distributions

Measures of niche overlap are used to assess the similarity or dissimilarity of two populations. Matusitas measure is one of commonly used niche overlap measures. We consider the problem of estimating Matusitas measure when samples are from multivariate normal distributions with unknown mean vectors and covariance matrices. Asymptotic variances and biases of Matusitas measure estimates are derived and bias reduction methods are proposed. Simulation results are shown to illustrate characteristics of the estimates and bias reduction methods.

Spontaneous flash communication of females in an Asian firefly

Fireflies are well known for the use of bioluminescence for sexual communication. In species using flash signals for pair formation, species and sexual identity are conferred by flash timing parameters such as flash duration, flash interval, flash number, and response delay. In dialog fireflies in North America, the male is the advertiser and the female is the responder. In these species, the male flash signal parameter varies depending on species, but the female flash signal parameter is limited only to response delay. However, in fireflies other than dialog fireflies, sexual flash communication is not well studied. Although many female-advertisement-like fireflies are reported, we have no confirmed case of sexual communication in a female-advertisement species. Here, we report the sexual flash communication of an Asian firefly, Luciola (Hotaria) parvula, in which the female flashes spontaneously. By using an electronic firefly, we confirm experimentally that males are specifically attracted to flashes with a female-specific flash duration. This is the first experimental report of sexual communication of a female advertiser in firefly communication. In this species, females call males usually with spontaneous flashes unlike dialog fireflies.

ML and REML estimation of Matusita's measure for two bivariate normal distributions with missing observations

SYNOPTIC ABSTRACT The measures of niche overlap are used to assess the similarity or dissimilarity of two populations. Matusitas measure is one of the commonly used niche overlap measures. We discuss the problem of estimating Matusitas measure when the niches are bivariate normal distributions with missing observations. Under the assumption of equal variance of two variates in each population, we consider four cases depending on whether the variances and correlations for the two populations are common or different. The plug-in estimates of Matusitas measure by the Maximum Likelihood (ML) estimates and the REstricted or REsidual Maximum Likelihood (REML) estimates for dispersion parameters are considered, their asymptotic variances and bias are derived, and bias correction methods are proposed. Simulation study shows that the plug-in estimate by the REMLE tends to have smaller MSE than that by the MLE and the bias correction reduces MSE considerably.

Inverse relationship and limiting forms of lagrange distributions

The basic Lagrange distribution is shown to be inversely related to some distribution obtained from the arrival distribution. Using this inverse relationship and the method of moments, we show that Lagrange distributions converge to normal distributions under some conditions and to inverse Gaussian distributions under other conditions. Although Consul and Shenton (1973) gave theorems aboutthe limiting forms of Lagrange distributions, they implicitly assume several conditions and their theorems do not hold in general We give counterexamples to Consul and Shentons theorems and examples of convergence to normal and to inverse Gaussian distributions.

Multivariate lagrange distributions and a subfamiliy

Second order moments about its means, i.e. the variances and covari-ances for multivariate Lagrange distributions are derived in a matrix form. A subfamily of multivariate Lagrange distributions which can be characterized as the distributions of customers served in a busy period in queues with some conditions are considered. Theorems about their probability functions, one of which is a multivariate generalization of a formula by Taka cs(1989). are given and the means and second order moments about its means are considered. As an example, a multivariate Borel-Tanner distribution is derived.