Journal of Data Science

Abstract: The Center for Neural Interface Design of the Biodesign Institute at Arizona State University conducted an experiment to investigate how the central nervous system controls hand orientation and movement direction during reach-to-grasp movements. ANOVA (Analysis of Variance), a conventional data analysis widely used in neural science, was performed to categorized different neural activities. Some preliminary studies on data analysis methods have shown that the principal assumption of ANOVA is violated and some characteristics of data are missing from taking the ratio of recorded data. To compensate the deficiency of ANOVA, ANCOVA (Analysis of covariance) is introduced in this paper. By considering neural firing counts and temporal intervals respectively, we expect to extract more useful information for determining the correlations among different types of neurons with motor behavior. Comparing to ANOVA, ANCOVA can be one step further to identify which direction or orientation is favored during which epoch. We find that a considerable number of neurons are involved in movement direction, hand orientation, or both combined, and some are significant in more than one epoch, which indicates there exists a network with unknown pathways connecting neurons in motor cortex throughout the entire movement. For the future studies we suggest to integrate this study into neural networking in order to simulate the whole reach-to-grasp process.

Abstract: It is well known that the ordinary least squares (OLS) regression estimator is not robust. Many robust regression estimators have been proposed and inferential methods based on these estimators have been derived. However, for two independent groups, let θj (X) be some conditional measure of location for the jth group, given X, based on some robust regression estimator. An issue that has not been addressed is computing a 1 − confidence interval for θ1(X) − θ2(X) in a manner that allows both within group and between group hetereoscedasticity. The paper reports the finite sample properties of a simple method for accomplishing this goal. Simulations indicate that, in terms of controlling the probability of a Type I error, the method performs very well for a wide range of situations, even with a relatively small sample size. In principle, any robust regression estimator can be used. The simulations are focused primarily on the Theil-Sen estimator, but some results using Yohai’s MM-estimator, as well as the Koenker and Bas sett quantile regression estimator, are noted. Data from the Well Elderly II study, dealing with measures of meaningful activity using the cortisol awakening response as a covariate, are used to illustrate that the choice between an extant method based on a nonparametric regression estimator, and the method suggested here, can make a practical difference.