A Smooth Simultaneous Confidence Corridor for the Mean of Sparse Functional Data

Universal Local Linear Kernel Estimators in Nonparametric Regression

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data. The theoretical results of the study are illustrated by simulations. An example of processing real medical data from the epidemiological cross-sectional study ESSE-RF is included. We compare the new estimators with the estimators best known for such studies.

Using Simultaneous Confidence Bands to Calculate the Margin of Error in Estimating Typical Biomechanical Waveforms

Studies of human movement usually collect data from multiple repetitions of a task and use the average of all movement trials to approximate the typical kinematics or kinetics pattern for each individual. Few studies report the expected accuracy of these estimated mean kinematics or kinetics waveforms for each individual. The purpose of this study is to demonstrate how simultaneous confidence bands, which is an approach to quantify uncertainty across an entire waveform based on limited data, can be used to calculate margin of error (MOE) for waveforms. Bilateral plantar pressure data were collected from 70 participants as they walked over 4 surfaces for an average of at least 300 steps per surface. The relationship between MOE and the number of steps included in the analysis was calculated using simultaneous confidence bands, and 3 methods commonly used for pointwise estimates: intraclass correlation, sequential averaging, and T-based MOE. The conventional pointwise approaches underestimated the number of trials required to estimate biomechanical waveforms within a desired MOE. Simultaneous confidence bands are an objective approach to more accurately estimate the relationship between the number of trials collected and the MOE in estimating typical biomechanical waveforms.

Simultaneous confidence corridors for mean functions in functional data analysis of imaging data

Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle an irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two-sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyze brain positron emission tomography data in two different studies. One data set used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

Prediction of working memory ability based on EEG by functional data analysis

BACKGROUND

There is always a demand for fast and accurate algorithms for EEG signal processing. Owing to the high sample rate, EEG signals usually come with a large number of sample points, making it difficult to predict the working memory ability in cognitive research with EEG.

NEW METHOD

Following well-designed experiments, the functional linear model provides a simple framework for regressions involving EEG signal predictors. The use of a data-driven basis in a linear structure naturally extends the standard linear regression model. The proposed approach utilizes B-spline approximation of functional principal components that greatly facilitates implementation.

RESULTS

Using LASSO feature selection, critical features have been extracted from eight frontal electrodes, and the R-square of 0.72 indicates rather strong linear association of actual observations and out-of-sample predictions.

COMPARISON WITH EXISTING METHODS

There does not seem to be any existing methods of predicting working memory ability from N-back task tests via EEG signals; the data-driven functional linear regression method proposed in this work is, to the best of our knowledge, the first of its kind.

CONCLUSIONS

The data analytics suggest that a multiple functional linear regression model for the predictive relationship between working memory ability and frontal activity of the brain is both feasible and accurate via EEG signal processing.