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In this article, we consider the problem of testing a linear hypothesis in a multivariate linear regression model which includes the case of testing the equality of mean vectors of several multivariate normal populations with common covariance matrix , the so-called multivariate analysis of variance or MANOVA problem. However, we have fewer observations than the dimension of the random vectors. Two tests are proposed and their asymptotic distributions under the hypothesis as well as under the alternatives are given under some mild conditions. A theoretical comparison of these powers is made.

In this paper, we study the problem of estimating the number of significant components in principal component analysis (PCA), which corresponds to the number of dominant eigenvalues of the covariance matrix of p variables. Our purpose is to examine the consistency of the estimation criteria AIC and BIC based on the model selection criteria by Akaike [In 2nd International Symposium on Information Theory (1973) 267-281, Akadémia Kiado] and Schwarz [Estimating the dimension of a model 6 (1978) 461-464] under a high-dimensional asymptotic framework. Using random matrix theory techniques, we derive sufficient conditions for the criterion to be strongly consistent for the case when the dominant population eigenvalues are bounded, and when the dominant eigenvalues tend to infinity. Moreover, the asymptotic results are obtained without normality assumption on the population distribution. Simulation studies are also conducted, and results show that the sufficient conditions in our theorems are essential.

Citation: Hamanaka T, Omata T, Sekimoto S, Sugiyama T, Fujikoshi Y. Bleb analysis by using anterior segment optical coherence tomography in two different methods of trabeculectomy. Invest Ophthalmol Vis Sci. 2013;54:6536-6541. DOI: 10.1167/iovs.13-12439 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 slitlamp 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 ¼ 3.0402, R ¼ 0.6401), yet no parameter was significant in group II (maximum R ¼ 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 ¼ 0.2037, 0.2314, R ¼ 0.4336, 0.4330) in group I. In group II, no parameter was significant, except CCD and/or LUSF (P ¼ 0.032). As to coincidence of IBAGS and AS-OCT parameters, height and extent in group I (P ¼ 0.000, P ¼ 0.000) and height in group II were statistically significant (P ¼ 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.