Robust template estimation for functional data with phase variability using band depth

2018 ◽  
Vol 125 ◽  
pp. 10-26
Author(s):  
Jason Cleveland ◽  
Weilong Zhao ◽  
Wei Wu
Keyword(s):  
Functional Data ◽  
Phase Variability ◽  
Band Depth

Simplicial band depth for multivariate functional data

2014 ◽  
Vol 8 (3) ◽  
pp. 321-338 ◽  
Author(s):  
Sara López-Pintado ◽  
Ying Sun ◽  
Juan K. Lin ◽  
Marc G. Genton
Keyword(s):  
Functional Data ◽  
Multivariate Functional Data ◽  
Band Depth

Comparison of Measures of Variability of Speech Movement Trajectories Using Synthetic Records

2005 ◽  
Vol 48 (2) ◽  
pp. 336-344 ◽  
Author(s):  
Jorge C. Lucero
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Accurate Assessment ◽  
Common Pattern ◽  
Temporal Alignment ◽  
Movement Trajectories ◽  
Phase Variability ◽  
Speech Research

In speech research, it is often desirable to assess quantitatively the variability of a set of speech movement trajectories. This problem is studied here using synthetic trajectories, which consist of a common pattern and terms representing amplitude and phase variability. The results show that a technique for temporal alignment of the records based on functional data analysis allows us to extract the pattern and variability terms as separate functions, with good approximation. Indices of amplitude and phase variability are defined, which provide a more accurate assessment of variability than previous approaches.

scholarly journals Bounding uncertainty in functional data: A case study

2021 ◽  
Vol 33 (1) ◽  
pp. 178-188
Author(s):  
Caleb King ◽  
Nevin Martin ◽  
James Derek Tucker
Keyword(s):  
Functional Data

scholarly journals Advanced Statistical Analysis of 3D Kinect Data: Mimetic Muscle Rehabilitation Following Head and Neck Surgeries Causing Facial Paresis

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 103
Author(s):  
Jan Kohout ◽  
Ludmila Verešpejová ◽  
Pavel Kříž ◽  
Lenka Červená ◽  
Karel Štícha ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Functional Data ◽  
Muscle Function ◽  
Evaluation Process ◽  
Multiple Logistic Regression ◽  
Facial Paresis ◽  
Kinect Camera ◽  
3D Camera ◽  
Mimetic Muscles ◽  
Data Analytic

An advanced statistical analysis of patients’ faces after specific surgical procedures that temporarily negatively affect the patient’s mimetic muscles is presented. For effective planning of rehabilitation, which typically lasts several months, it is crucial to correctly evaluate the improvement of the mimetic muscle function. The current way of describing the development of rehabilitation depends on the subjective opinion and expertise of the clinician and is not very precise concerning when the most common classification (House–Brackmann scale) is used. Our system is based on a stereovision Kinect camera and an advanced mathematical approach that objectively quantifies the mimetic muscle function independently of the clinician’s opinion. To effectively deal with the complexity of the 3D camera input data and uncertainty of the evaluation process, we designed a three-stage data-analytic procedure combining the calculation of indicators determined by clinicians with advanced statistical methods including functional data analysis and ordinal (multiple) logistic regression. We worked with a dataset of 93 distinct patients and 122 sets of measurements. In comparison to the classification with the House–Brackmann scale the developed system is able to automatically monitor reinnervation of mimetic muscles giving us opportunity to discriminate even small improvements during the course of rehabilitation.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

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