Approximate Asymptotic Distribution of Locally Most Powerful Invariant Test for Independence: Complex Case

2018 ◽  
Vol 64 (3) ◽  
pp. 1784-1799 ◽  
Author(s):  
Yu-Hang Xiao ◽  
Lei Huang ◽  
Junhao Xie ◽  
Hing Cheung So
2020 ◽  
Author(s):  
Mili Dhar ◽  
Jennifer Elias ◽  
Benjamin Field ◽  
Sunil Zachariah ◽  
Julian Emmanuel

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.


2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.


2020 ◽  
Vol 133 (2) ◽  
pp. 521-529 ◽  
Author(s):  
Vivek P. Bodani ◽  
Gerben E. Breimer ◽  
Faizal A. Haji ◽  
Thomas Looi ◽  
James M. Drake

OBJECTIVEEndoscopic resection of third-ventricle colloid cysts is technically challenging due to the limited dexterity and visualization provided by neuroendoscopic instruments. Extensive training and experience are required to master the learning curve. To improve the education of neurosurgical trainees in this procedure, a synthetic surgical simulator was developed and its realism, procedural content, and utility as a training instrument were evaluated.METHODSThe simulator was developed based on the neuroimaging (axial noncontrast CT and T1-weighted gadolinium-enhanced MRI) of an 8-year-old patient with a colloid cyst and hydrocephalus. Image segmentation, computer-aided design, rapid prototyping (3D printing), and silicone molding techniques were used to produce models of the skull, brain, ventricles, and colloid cyst. The cyst was filled with a viscous fluid and secured to the roof of the third ventricle. The choroid plexus and intraventricular veins were also included. Twenty-four neurosurgical trainees performed a simulated colloid cyst resection using a 30° angled endoscope, neuroendoscopic instruments, and image guidance. Using a 19-item feedback survey (5-point Likert scales), participants evaluated the simulator across 5 domains: anatomy, instrument handling, procedural content, perceived realism, and confidence and comfort level.RESULTSParticipants found the simulator’s anatomy to be highly realistic (mean 4.34 ± 0.63 [SD]) and appreciated the use of actual instruments (mean 4.38 ± 0.58). The procedural content was also rated highly (mean 4.28 ± 0.77); however, the perceived realism was rated slightly lower (mean 4.08 ± 0.63). Participants reported greater confidence in their ability to perform an endoscopic colloid cyst resection after using the simulator (mean 4.45 ± 0.68). Twenty-three participants (95.8%) indicated that they would use the simulator for additional training. Recommendations were made to develop complex case scenarios for experienced trainees (normal-sized ventricles, choroid plexus adherent to cyst wall, bleeding scenarios) and incorporate advanced instrumentation such as side-cutting aspiration devices.CONCLUSIONSA patient-specific synthetic surgical simulator for training residents and fellows in endoscopic colloid cyst resection was successfully developed. The simulator’s anatomy, instrument handling, and procedural content were found to be realistic. The simulator may serve as a valuable educational tool to learn the critical steps of endoscopic colloid cyst resection, develop a detailed understanding of intraventricular anatomy, and gain proficiency with bimanual neuroendoscopic techniques.


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