Takakazu Sugiyama

Bleb analysis by using anterior segment optical coherence tomography in two different methods of trabeculectomy.

PURPOSE To investigate the correlation between bleb morphology and IOP control via the modified Indiana Bleb Appearance Grading Scale (IBAGS) and anterior-segment optical coherence tomography (AS-OCT) in two different trabeculectomy (TLE) groups. METHODS This study involved 94 eyes with primary open angle glaucoma that underwent two different TLE methods: limbal-based TLE (group I, 62 eyes) and fornix-based TLE (group II, 32). IOP control was defined as successful with an IOP ≤ 20 mm Hg and ≥20% reduction of preoperative IOP. IBAGS and various parameters of the bleb height, extent, wall thickness, ciliochoroidal detachment (CCD), and lake under the scleral flap (LUSF) were obtained by slit-lamp and AS-OCT, respectively. Correlation between IOP control and IBAGS/AS-OCT parameters were assessed by SAS. RESULTS Both groups had the same success rate. As to correlation between IOP control and IBAGS, extent and Seidel were the best-paired parameters in group I (Cp = 3.0402, R = 0.6401), yet no parameter was significant in group II (maximum R = 0.1599). As to correlation between IOP control and AS-OCT, the combinations of height, extent, and the minimum value of bleb wall thickness were significant (Cp = 0.2037, 0.2314, R = 0.4336, 0.4330) in group I. In group II, no parameter was significant, except CCD and/or LUSF (P = 0.032). As to coincidence of IBAGS and AS-OCT parameters, height and extent in group I (P = 0.000, P = 0.000) and height in group II were statistically significant (P = 0.020). CONCLUSIONS IOP control in limbal-based TLE seemed to be more dependent on the large size and thinned-wall bleb than that in fornix-based TLE.

Correlation analysis of principal components from two populations

We investigate a correlation coefficient of principal components from two sets of variables. Using perturbation expansion, we get a limiting distribution of the correlation. In addition, we obtain a limiting distribution of the Fishers z transformation of the above correlation. Additionally, we verify the accuracy of the limiting distributions using Monte Carlo simulations. Finally in this study, we present two examples and a bootstrap estimation.

On the permutation test in canonical correlation analysis

In canonical correlation analysis, we are interested in testing whether the @ath canonical correlation coefficient is some number, especially the first canonical correlation coefficient. In this paper, we try the permutation test in canonical correlation analysis and suggest some test statistics.

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 u...

Improved approximations to distributions of the largest and the smallest latent roots of a wishart matrix

SummaryNormalizing transformations of the largest and the smallest latent roots of a sample covariance matrix in a normal sample are obtained, when the corresponding population roots are simple. Using our results, confidence intervals for population roots may easily be constructed. Some numerical comparisons of the resulting approximations are made in a bivariate case, based on exact values of the probability integral of latent roots.

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.

Asymptotic Distributions and Confidence Intervals of Component Loading in Principal Component Analysis

In principal component analysis, it is quite useful to know the values of a correlation coefficient between a principal component and an original variable. We seek for knowing a meaning of each principal component from their values. However, we do not know how reliable the value of the component loading is. For this purpose we investigate the distribution of the component loading. But it is difficult to obtain its exact distribution. Therefore, we derive an asymptotic expansion for the distribution of the component loading, and also construct the confidence intervals from the result.

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.

Asymptotic Distribution of the Contribution Ratio in High-Dimensional Principal Component Analysis

Abstract In principal component analysis we use the sample cumulative contribution ratio as an estimate of the population cumulative contribution ratio which is a proportion of information condensed into the first several principal components. The main purpose of this paper is to derive an asymptotic distribution of the cumulative contribution ratio in a high-dimensional situation where both the dimension and the sample size are large. Its asymptotic distribution is derived under a spiked model in which the variances of the remainder population principal components are assumed to be equal and small. We consider its logit transformation which is useful in a situation where the population cumulative contribution ratio is high or low. The corresponding large sample results are also summarized with a generalization. Numerical simulation revealed that our new approximation is more accurate than the classical large sample approximation as the dimension increases.

Large sample approximations for the LR statistic for equality of the smallest eigenvalues of a covariance matrix under elliptical population

This paper is concerned with large sample approximations of the LR statistic for testing the hypothesis that the smallest eigenvalues of a covariance matrix are equal. Under a normal population Lawley [1956. Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43, 128-136.] and Fujikoshi [1977. An asymptotic expansion for the distributions of the latent roots of the Wishart matrix with multiple population roots. Ann. Inst. Statist. Math. 29, 379-387.] obtained a Bartlett-correction factor and an asymptotic expansion for the LR statistic, respectively, when the sample size is large. In this paper we extend the Bartlett correction factor to an elliptical population. The accuracy of our approximations is examined through simulation experiments.