High dimensional discriminant rules with shrinkage estimators of covariance matrix and mean vector

Linear discriminant analysis is a typical method used in the case of large dimension and small samples. There are various types of linear discriminant analysis methods, which are based on the estimations of the covariance matrix and mean vectors. Although there are many methods for estimating the inverse matrix of covariance and the mean vectors, we consider shrinkage methods based on non-parametric approach. In the case of the precision matrix, the methods based on either the sparsity structure or the data splitting are considered. Regarding the estimation of mean vectors, nonparametric empirical Bayes (NPEB) estimator and nonparametric maximum likelihood estimation (NPMLE) methods are adopted which are also called f-modeling and g-modeling, respectively. We analyzed the performances of linear discriminant rules which are based on combined estimation strategies of the covariance matrix and mean vectors. In particular, we present a theoretical result on the performance of the NPEB method and compare that with the results from other methods in previous studies. We provide simulation studies for various structures of covariance matrices and mean vectors to evaluate the methods considered in this paper. In addition, real data examples such as gene expressions and EEG data are presented.Comment: 39 pages, 3 figure

An Exact and Near-Exact Distribution Approach to the Behrens–Fisher Problem

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1A01100526). Publisher Copyright: © 2022 by the authors.The Behrens–Fisher problem occurs when testing the equality of means of two normal distributions without the assumption that the two variances are equal. This paper presents approaches based on the exact and near-exact distributions for the test statistic of the Behrens–Fisher problem, depending on different combinations of even or odd sample sizes. We present the exact distribution when both sample sizes are odd and the near-exact distribution when one or both sample sizes are even. The near-exact distributions are based on a finite mixture of generalized integer gamma (GIG) distributions, used as an approximation to the exact distribution, which consists of an infinite series. The proposed tests, based on the exact and the near-exact distributions, are compared with Welch’s t-test through Monte Carlo simulations, in particular for small and unbalanced sample sizes. The results show that the proposed approaches are competent solutions to the Behrens–Fisher problem, exhibiting precise sizes and better powers than Welch’s approach for those cases. Numerical studies show that the Welch’s t-test tends to be a bit more conservative than the test statistics based on the exact or near-exact distribution, in particular when sample sizes are small and unbalanced, situations in which the proposed exact or near-exact distributions obtain higher powers than Welch’s t-test.publishersversionpublishe

Controller Area Network With Flexible Data Rate (CAN FD) Eye Diagram Prediction

A method for predicting the eye diagram for a controller area network with a flexible data rate (CAN FD) is proposed in this article. A CAN FD changes a data rate according to the status to overcome the limitation of latency. In other words, when data to be transmitted are accumulated, the CAN FD increases the data rate up to 5 Mb/s. The CAN FD has a bus topology consisting of multiple electronic control units, which results in a significant amount of signal reflection. Thus, the above causes the signal integrity analysis uncertain. To avoid this, this article proposes a simplified model for the CAN FD and the eye diagram prediction method based on it. The proposed method has the deterministic and statistical: the deterministic part uses an iterative single bit response method for bit probabilities of a CAN FD packet, and the statistical part uses a modified double edge response method for the flexible data rate. For verification, this article compares the predicted eye diagram to the measured eye diagram, and they are nearly the same when the CAN FD operates at the nominal data rate of 1 and optional data rate of 2 Mb/s