On a statistic useful in dimensionality reduction in multivariable linear stochastic system

In this paper we study the sampling properties of a test statistic which has important applications in the area of linear stochastic control systems with multi-inputs and multi-outputs. The statistic is the ratio of a partial sum of the eigenvalues of a sample covariance matrix and its trace. It turns out that using a method due to Sugiura we may derive a useful approximation for its distribution up to and including terms of order l/n, where n denotes the appropriate size. Numerical illustrations using real data are given.     

Seasonality and vertical structure of light-attracted insect communities in a dipterocarp forest in Sarawak

Nocturnal flying insects were collected monthly for 13 months using ultra violet light-traps set at various vertical levels in a weakly-seasonal, tropical lowland dipterocarp forest in Sarawak, Malaysia. Abundance, faunal composition, size distribution and guild structure of these samples were analyzed with respect to temperal and vertical distributions. The nocturnal flying insect community in the canopy level was highly dominated by fig wasps (84%) in individual number, and by scarabaeid beetles (28%) in weight. A principal component analysis on monthly catches detected non-random, seasonal trends of insect abundance. The first two principal trends were an alternation of wetter (September to January) and less wet seasons (February to August) and an alternation between the least wet (January to March) and the other seasons. Many insect groups were less abundant in the least wet season than the other seasons, whilst inverse patterns were found in Scarabaeidae and Tenebrionidae. Significantly positive and negative correlations between monthly catch and rainfall were detected only in ovule-feeders and in phloem-feeders, respectively. Delayed, significant negative correlations between monthly catch and 1–3 month preceding rainfall were more frequently detected in phytophages, phloem-feeders, seed-feeders, wood-borers and scavengers. The peak in abundance along vertical levels were found at the canopy level (35 m) for phloem-, ovule-, seed-, root-, fungal-feeders and nectar collectors, at an upper subcanopy level (25 m) for scavengers and aquatic predators, and at a middle subcanopy level (17 m) for ants. Catches at the emergent level (45 m) did not exceed those at the canopy level.     

Exact power comparison of three criteria to assess the independence between two sets of variates

Powers of the three criteria are evaluated for testing the hypothesis of the independence between a -set and a q-set of variates in a (p + q) -variate normal population. They are: (1) the likelihood ratio type criterion, Wt (2) the largest root criterion, r1, and (3) criterion of the sum of roots, V. For p= 2, Pillai and Jayachandran, and others have studied for the restricted range of the alternative hypothesis. Recently the power of the largest root was investigated in detail by Sugiyama and %%. In this paper, their power functions are compared in a wide range of the alternative hypotheses. The powers of rl and V are locally optimum, but the W shows a large power in a wide range.     

Permutation Test for Equality of Individual an Eigenvalue from a Covariance Matrix in High-Dimension

A test statistic for examining the equality of an individual eigenvalue in two populations of high dimension is proposed. The asymptotic distribution of the proposed statistic is derived and the validity of the permutation test is discussed. Simulations were used to investigate the power of the suggested statistic. The proposed statistic is applied to hand measurement data on white and aboriginal Australians to test the equality of the eigenvalues.     

Recurrence relations of coefficients of the generalized hypergeometric function in multivariate analysis

James(1960) defined the zonal polynomials and used it to represent the joint distributions of latent roots of VVisfiart matrix. The zonal polviionnals played an important role to define the generalized hypergeometric function of symmetric matrix argument Since then, many density functions and moments based on Wishart matrix have been expressed in terms of the generalized hy¬pergeometric Function. The purpose of this paper is to get the recurrence relations for the coefficients of it. In Section 1 we derive a partial differen¬tial equations having the generalized hypergeometric function as the unique solution. Then we ubtain the recurrence relations until order 7 in Section 2.     

A Variable Selection Criterion for Two Sets of Principal Component Scores in Principal Canonical Correlation Analysis

Canonical correlation analysis (CCA) is often used to analyze the correlation between two random vectors. However, sometimes interpretation of CCA results may be hard. In an attempt to address these difficulties, principal canonical correlation analysis (PCCA) was proposed. PCCA is CCA between two sets of principal component (PC) scores. We consider the problem of selecting useful PC scores in CCA. A variable selection criterion for one set of PC scores has been proposed by Ogura (2010), here, we propose a variable selection criterion for two sets of PC scores in PCCA. Furthermore, we demonstrate the effectiveness of this criterion.     

战后日本交通基础设施发展与地区间收入差距问题研究

战后,日本经济经过了恢复、增长、飞速发展的这样一个轨迹,其中交通基础设施的发展也是关系到日本全国经济发展的一个重要因素。本文旨在探讨战后日本交通基础设施建设的同时,试图从原有的地区间的收入问题、日本政府所采取的政策,以及地区间收入差距与交通的关系中梳理出交通基础设施建设对于促进日本经济发展及其在缩小地区间收入差距所起到的作用。     

Power of largest root on canonical correlation

We consider the testing hypothesis that two random vectors of p and q components are independent in canonical correlation analysis. In this paper we investigate the powers of the test based on the largest root criterion. As the exact distribution are expressed by the zonal polynomials, the computation is possible only for p=2, and also it is necessary to calculate using quadruplex precision because we lose the significance by subtraction. So in Table I we obtain the percentage points of the largest root criterion for the computation of the quadruplex precision. Then we calculate the power when p=2 and q = 3 to 11 (2). The results show that for the fixed n–q the power becomes smaller when q increases, and for the fixed p1 of the alternative hypothesis (p1, P2) the power does not become significantly large when P2 increases. We can also find the sample size required for the power agnist some alternative hypothesis to be about 0.9. the numerical results may be useful to find the quality of approximation by using formula of the asyptotic distribution.