PARAMETRIC CONDITIONAL MEAN INFERENCE WITH FUNCTIONAL DATA APPLIED TO LIFETIME INCOME CURVES

2021 ◽  
Author(s):  
Jin Seo Cho ◽  
Peter C. B. Phillips ◽  
Juwon Seo
Keyword(s):  
Functional Data ◽  
Conditional Mean ◽  
Lifetime Income

scholarly journals Two-Dimensional Sampling-Recovery Algorithm of a Realization of Gaussian Processes on the Input and Output of Linear Systems

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1079
Author(s):  
Vladimir Kazakov ◽  
Mauro A. Enciso ◽  
Francisco Mendoza
Keyword(s):  
Gaussian Processes ◽  
Research Method ◽  
General Algorithm ◽  
Two Dimensional ◽  
Recovery Algorithm ◽  
Conditional Mean ◽  
Quality Of Recovery ◽  
Input And Output ◽  
Statistical Relationships

Based on the application of the conditional mean rule, a sampling-recovery algorithm is studied for a Gaussian two-dimensional process. The components of such a process are the input and output processes of an arbitrary linear system, which are characterized by their statistical relationships. Realizations are sampled in both processes, and the number and location of samples in the general case are arbitrary for each component. As a result, general expressions are found that determine the optimal structure of the recovery devices, as well as evaluate the quality of recovery of each component of the two-dimensional process. The main feature of the obtained algorithm is that the realizations of both components or one of them is recovered based on two sets of samples related to the input and output processes. This means that the recovery involves not only its own samples of the restored realization, but also the samples of the realization of another component, statistically related to the first one. This type of general algorithm is characterized by a significantly improved recovery quality, as evidenced by the results of six non-trivial examples with different versions of the algorithms. The research method used and the proposed general algorithm for the reconstruction of multidimensional Gaussian processes have not been discussed in the literature.

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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