Robust optimal estimation of location from discretely sampled functional data

Estimating location is a central problem in functional data analysis, yet most current estimation procedures either unrealistically assume completely observed trajectories or lack robustness with respect to the many kinds of anomalies one can encounter in the functional setting. To remedy these deficiencies we introduce the first class of optimal robust location estimators based on discretely sampled functional data. The proposed method is based on M‐type smoothing spline estimation with repeated measurements and is suitable for both commonly and independently observed trajectories that are subject to measurement error. We show that under suitable assumptions the proposed family of estimators is minimax rate optimal both for commonly and independently observed trajectories and we illustrate its highly competitive performance and practical usefulness in a Monte‐Carlo study and a real‐data example involving recent Covid‐19 data. [ FROM AUTHOR] Copyright of Scandinavian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

A Frequency Estimation Scheme Based on Gaussian Average Filtering Decomposition and Hilbert Transform: With Estimation of Respiratory Rate as an Example.

Frequency estimation plays a critical role in vital sign monitoring. Methods based on Fourier transform and eigen-analysis are commonly adopted techniques for frequency estimation. Because of the nonstationary and time-varying characteristics of physiological processes, time-frequency analysis (TFA) is a feasible way to perform biomedical signal analysis. Among miscellaneous approaches, Hilbert-Huang transform (HHT) has been demonstrated to be a potential tool in biomedical applications. However, the problems of mode mixing, unnecessary redundant decomposition and boundary effect are the common deficits that occur during the procedure of empirical mode decomposition (EMD) or ensemble empirical mode decomposition (EEMD). The Gaussian average filtering decomposition (GAFD) technique has been shown to be appropriate in several biomedical scenarios and can be an alternative to EMD and EEMD. This research proposes the combination of GAFD and Hilbert transform that is termed the Hilbert-Gauss transform (HGT) to overcome the conventional drawbacks of HHT in TFA and frequency estimation. This new method is verified to be effective for the estimation of respiratory rate (RR) in finger photoplethysmography (PPG), wrist PPG and seismocardiogram (SCG). Compared with the ground truth values, the estimated RRs are evaluated to be of excellent reliability by intraclass correlation coefficient (ICC) and to be of high agreement by Bland-Altman analysis.

Uncertainty Quantification for Epidemic Risk Management: Case of SARS-CoV-2 in Morocco.

In this paper, we propose a new method for epidemic risk modelling and prediction, based on uncertainty quantification (UQ) approaches. In UQ, we consider the state variables as members of a convenient separable Hilbert space, and we look for their representation in finite dimensional subspaces generated by truncations of a suitable Hilbert basis. The coefficients of the finite expansion can be determined by approaches established in the literature, adapted to the determination of the probability distribution of epidemic risk variables. Here, we consider two approaches: collocation (COL) and moment matching (MM). Both are applied to the case of SARS-CoV-2 in Morocco, as an epidemic risk example. For all the epidemic risk indicators computed in this study (number of detections, number of deaths, number of new cases, predictions and human impact probabilities), the proposed models were able to estimate the values of the state variables with precision, i.e., with very low root mean square errors (RMSE) between predicted values and observed ones. Finally, the proposed approaches are used to generate a decision-making tool for future epidemic risk management, or, more generally, a quantitative disaster management approach in the humanitarian supply chain.

Analyzing Jo-Ha-Kyu Mechanism in Japanese Traditional Performing Art Ningyo Joruri

IoT devices that connect people without physical contact become more and more important after the COVID-19 impact. However, strange appearances and movements performed by IoT devices (interactive humanoid robots) cause human discomfort, so-called the uncanny valley, preventing widespread use of humanoid IoT devices. On the contrary, a Japanese traditional performing art named Ningyo Joruri (puppet theater) is recognized as a UNESCO intangible cultural heritage, and the sophisticated puppet motions and its unique music style somehow can avoid causing human discomfort even if the appearance of puppets is close enough to humans. One of the most important factors in empathizing humans with the puppet without uncomfortable is the modulation technique of both music tempo and motion speed known as Jo-Ha-Kyu. In this study, we analyzed Ningyo Joruri based on the Jo-Ha-Kyu mechanism, which is an art concept adopted in the puppet theater to interact with audiences according to modulation of the tempo. First, we obtained puppet movements using motion capture systems with the music. Second, we detected the changing tempo in Ningyo Joruri using the deep learning method to demonstrate the Jo-Ha-Kyu mechanism quantitatively. Finally, we showed the correlation of Jo-Ha-Kyu between Ningyo Joruri music and puppet manipulation techniques in the frequency domain using the Hilbert Huang transform. Our results revealed that low-frequency movements play an important role in synchronizing motion to the tempo of corresponding music, presenting novel knowledge to motion designers for humanoid robots IoT devices. © 2022 IEEE.

Improvement of Split-Step Forward Milstein Schemes for SODEs Arising in Mathematical Physics

In the present investigation, new explicit approaches by the Milstein method and increment function of the Jacobian derivative of the drift coefficient are designed. Several numerical tests such as Cox–Ingersoll–Ross process, stochastic Brusselator, and Davis-Skodje system are presented to illustrate the accuracy and the efficiency of our schemes. Furthermore, we show that the strong convergence rate of our procedures is approximately one.

Robust optimal estimation of location from discretely sampled functional data

Estimating location is a central problem in functional data analysis, yet most current estimation procedures either unrealistically assume completely observed trajectories or lack robustness with respect to the many kinds of anomalies one can encounter in the functional setting. To remedy these deficiencies we introduce the first class of optimal robust location estimators based on discretely sampled functional data. The proposed method is based on M-type smoothing spline estimation with repeated measurements and is suitable for both commonly and independently observed trajectories that are subject to measurement error. We show that under suitable assumptions the proposed family of estimators is minimax rate optimal both for commonly and independently observed trajectories and we illustrate its highly competitive performance and practical usefulness in a Monte-Carlo study and a real-data example involving recent Covid-19 data. (PsycInfo Database Record (c) 2022 APA, all rights reserved)

A sentiment-based modeling and analysis of stock price during the COVID-19: U- and Swoosh-shaped recovery.

In the aftermath of stock market crash due to COVID-19, not all sectors recovered in the same way. Recently, a stock price model is proposed by Mahata et al. (2021) that describes V- and L-shaped recovery of the stocks and indices, but fails to simulate the U- and Swoosh-shaped recovery that arises due to sharp fall, continuation at the low price and followed by quick recovery, slow recovery for longer period, respectively. We propose a modified model by introducing a new parameter θ = + 1 , 0 , - 1 to quantify investors' positive, neutral and negative sentiments, respectively. The model explains movement of sectoral indices with positive financial anti-fragility ( ϕ ) showing U- and Swoosh-shaped recovery. Simulation using synthetic fund-flow with different shock lengths, ϕ , negative sentiment period and portion of fund-flow during recovery period show U- and Swoosh-shaped recovery. It shows that recovery of indices with positive ϕ becomes very weak with extended shock and negative sentiment period. Stocks with higher ϕ and fund-flow show quick recovery. Simulation of Nifty Bank, Nifty Financial and Nifty Realty show U-shaped recovery and Nifty IT shows Swoosh-shaped recovery. Simulation results are consistent with stock price movement. The estimated time-scale of shock and recovery of these indices are also consistent with the time duration of change of negative sentiment from the onset of COVID-19. We conclude that investors need to evaluate sentiment along with ϕ before investing in stock markets because negative sentiment can dampen the recovery even in financially anti-fragile stocks.

Verification results for age-structured models of economic-epidemics dynamics.

In this paper we propose a macro-dynamic age-structured set-up for the analysis of epidemics/economic dynamics in continuous time. The resulting optimal control problem is reformulated in an infinite dimensional Hilbert space framework where we perform the basic steps of dynamic programming approach. Our main result is a verification theorem which allows to guess the feedback form of optimal strategies. This will be a departure point to discuss the behavior of the models of the family we introduce and their policy implications.