Correction to: Inference on high-dimensional mean vectors under the strongly spiked eigenvalue model

The article Inference on high-dimensional mean vectors under the strongly spiked eigenvalue model

Ridgelized Hotelling’s T2 test on mean vectors of large dimension

In this paper, a ridgelized Hotelling’s [Formula: see text] test is developed for a hypothesis on a large-dimensional mean vector under certain moment conditions. It generalizes the main result of Chen et al. [A regularized Hotelling’s [Formula: see text] test for pathway analysis in proteomic studies, J. Am. Stat. Assoc. 106(496) (2011) 1345–1360.] by relaxing their Gaussian assumption. This is achieved by establishing an exact four-moment theorem that is a simplified version of Tao and Vu’s [Random matrices: universality of local statistics of eigenvalues, Ann. Probab. 40(3) (2012) 1285–1315] work. Simulation results demonstrate the superiority of the proposed test over the traditional Hotelling’s [Formula: see text] test and its several extensions in high-dimensional situations.

ROBUST PORTFOLIO SELECTION WITH CLUSTERING BASED ON BUSINESS SECTOR OF STOCKS

In recent years there have been numerous studies on portfolio selection using cluster analysis in conjunction with Markowitz model which used mean vectors and covariance matrix that are estimated from a highly volatile data. This study presents a more robust way of portfolio selection where stocks are grouped into clusters based on business sector of stocks. A representative from each cluster is selected from each cluster using Sharpe ratio to construct a portfolio and then optimized using robust FCMD and S-estimation. Calculation Sharpe ratio showed that this method works efficiently on large number of data while also robust against outlier in comparison to k-mean clustering. Implementation of this method on stocks listed on the Indonesia Stock Exchange, which included in the LQ-45 indexed for the period of August 2017 to July 2018 showed that portfolio performance obtained using clustering base on business sector of stocks combine with robust FMCD estimation is outperformed the other possible combination of the methods.

A supervised similarity measure for link prediction based on KNN

As a research hotspot of complex network analysis, link prediction has received growing attention from various disciplines. Link prediction intends to determine the connecting probability of latent links based on the observed structure information. To this end, a host of similarity-based and learning-based link prediction methods have been proposed. To attain stable prediction performance on diverse networks, this paper proposes a supervised similarity-based method, which absorbs the advantages of both kinds of link prediction methods. In the proposed method, to capture the characteristics of a node pair, a collection of structural features is extracted from the network to represent the node pair as a vector. Then, the positive and negative [Formula: see text]-nearest neighbors are searched from existing and nonexisting links, respectively. The connection likelihood of a node pair is measured according to its distances to the local mean vectors of positive and negative [Formula: see text]-nearest neighbors. The prediction performance of the proposed method is experimentally evaluated on 10 benchmark networks. The results show that the proposed method is superior to the compared methods in terms of accuracy and stableness.

Sensory Input Modulates Microsaccades during Heading Perception

Microsaccades are small eye movements produced during attempted fixation. During locomotion, the eyes scan the environment; the gaze is not always directed to the focus of expansion of the optic flow field. We sought to investigate whether the microsaccadic activity was modulated by eye position during the view of radial optic flow stimuli, and if the presence or lack of a proprioceptive input signal may influence the microsaccade characteristics during self-motion perception. We recorded the oculomotor activity when subjects were either standing or sitting in front of a screen during the view of optic flow stimuli that simulated specific heading directions with different gaze positions. We recorded five trials of each stimulus. Results showed that microsaccade duration, peak velocity, and rate were significantly modulated by optic flow stimuli and trial sequence. We found that the microsaccade rate increased in each condition from trial 1 to trial 5. Microsaccade peak velocity and duration were significantly different across trials. The analysis of the microsaccade directions showed that the different combinations of optic flow and eye position evoked non-uniform directions of microsaccades in standing condition with mean vectors in the upper-left quadrant of the visual field, uncorrelated with optic flow directions and eye positions. In sitting conditions, all stimuli evoked uniform directions of microsaccades. Present results indicate that the proprioceptive signals when the subjects stand up creates a different input that could alter the eye-movement characteristics during heading perceptions.

Modified Likelihood Ratio Test for Sub-mean Vectors with Two-step Monotone Missing Data in Two-sample Problem

This article deals with the problem of testing for two normal sub-mean vectors when the data set have two-step monotone missing observations. Under the assumptions that the population covariance matrices are equal, we obtain the likelihood ratio test (LRT) statistic. Furthermore, an asymptotic expansion for the null distribution of the LRT statistic is derived under the two-step monotone missing data by the perturbation method. Using the result, we propose two improved statistics with good chi-squared approximation. One is the modified LRT statistic by Bartlett correction,and the other is the modified LRT statistic using the modification coefficient by linear interpolation. The accuracy of the approximations are investigated by using a Monte Carlo simulation. The proposed methods are illustrated using an example.