Interval Data Research Articles

Nonparametric inference for interval data using kernel methods

ABSTRACT Symbolic data have become increasingly popular in the era of big data. In this paper, we consider density estimation and regression for interval-valued data, a special type of symbolic data, common in astronomy and official statistics. We propose kernel estimators with adaptive bandwidths to account for variability of each interval. Specifically, we derive cross-validation bandwidth selectors for density estimation and extend the Nadaraya–Watson estimator for regression with interval data. We assess the performance of the proposed methods in comparison with existing kernel methods by extensive simulation studies and real data analysis.

Secondary frequency control strategy considering DoS attacks for MTDC system

The utilization of communication networks brings benefits to frequency support strategies for multi-terminal high voltage direct current (MTDC) systems, yet leads to the systems facing cyber security risks. In particular, the denial of service (DoS) attacks will cause loss of measured signals and make the MTDC system unstable. This paper is concerned with the secondary frequency control problem defending DoS attacks in MTDC systems. Focusing on energy-limited and periodic DoS attacks, a Bernoulli process model is firstly adopted, and the control objective considering DoS attacks is built. Thereafter a switching scheme of the attacked station from droop control to secondary frequency regulation is devised for frequency support of MTDC systems. Two strategies respectively using the reference value and the data of the previous time interval are then proposed to compensate for the lost data due to DoS attacks. Four scenarios are simulated on a four-terminal MTDC system to verify the effectiveness of the two proposed solutions. The results show that, if the system is in equilibrium states during DoS attacks, both of the two proposed strategies are effective. Whereas the solution using the data of the previous time interval has better performances in the subsequent regulation process after load disturbance. • A switching control mechanism is devised for restoring the frequency of MTDC systems. • DoS attack will seriously affect the control process of MTDC systems. • Strategy(1) can be utilized when the system is in operating phase of steady state. • Strategy(2) has a better performance in the operating state when the system changes.

Sequential Malmquist-Luenberger productivity index for interval data envelopment analysis

<p style='text-indent:20px;'>Data envelopment analysis (DEA) based productivity indexes models are widely applied to evaluate the productivity of decision-making units over a period. This study proposes a productivity index for evaluating environmentally sensitive productivity growth while excluding the possibility of spurious technical regress. This innovative index has been created by combining directional distance functions, sequential DEA, undesirable data, and the concept of interval DEA. With this combination, the traditional sequential Malmquist-Luenberger productivity index (SMLPI) has been reformulated as an interval DEA problem to present a novel productivity index named interval SMLPI. We propose a decomposition of the developed index utilizing both constant returns to scale and variable returns to scale frontiers as the benchmark, which allows us to quantify scale efficiency change with interval data. To exhibit the capability of the proposed extension of SMLPI, we model a framework for Indian commercial banks and measure productivity change intervals for twenty-one banks from 2011 to 2018. The empirical findings elucidate that the scale efficiency change plays an essential role in driving productivity change. ICICI Bank had the highest average marginal productivity gain of 1.5007 between 2011 and 2018, whereas Karur Vysya bank had the highest average marginal productivity decline of 0.9411.</p>

Application of FY-4B Geostationary Meteorological Satellite in Grassland Fire Dynamic Monitoring

In this study, the channel data related to fire point identification of Advanced Geostationary Radiation Imager on Fengyun-4B (FY-4B/AGRI) and Advanced Meteorological Imager on GEO-KOMPSAT 2A (GK-2A/AMI) were cross-compared. A total of 267 sampling points in China (Guangdong, Guangxi, Guizhou, Yunnan, Hainan) were selected to carry out fine positioning correction on the data in different elevation intervals. Then, a fire monitoring algorithm based on FY-4B was proposed, in which the self-adaptive threshold adjustment of the underlying surface parameters and the reprocessing module of fire point identification were added. The algorithm can realize the high-precision and stable monitoring of fire. The continuous dynamic monitoring was carried out using the grassland fire Mongolia from April 18 to 20, 2022 as an example. The results showed that the parameters of FY-4B/AGRI and GK2A/AMI channels have high consistency. The root mean square error (RMSE) of reflection channel was 1.33%, and the maximum RMSE of brightness temperature channel was less than 1.3 Kelvin (K). Through the positioning analysis in different elevation intervals, the average longitude offset of FY-4B satellite data was -0.5°–0° and the average latitude offset was -0.9°–0.6°. Overall, these findings indicate that the high-frequency observations of FY-4B can be fully utilized to monitor forest and grassland fires, which can continuously track the dynamic evolution of fire and can distinguish the spatial distribution of different fire intensities in large-scale fire field.

Electrophysiological study in chagasics with syncope and conduction disorder.

Investigation of syncope involves the use of electrophysiological study, particularly in patients with cardiac conduction disorder. There is conflicting evidence about the role of electrophysiological study in patients with Chagas disease. The objective of this study was to evaluate the electrophysiological study findings in patients with Chagas disease and bundle branch block and/or divisional block presenting with syncope. This is a retrospective study of patients with Chagas disease and cardiac conduction disorder who underwent electrophysiological study from 2017 to 2021 for the investigation of syncope in a tertiary hospital in São Paulo, Brazil. Those with non-interpretable ECG, known coronary artery disease, and/or other cardiomyopathies were excluded. HV interval and electrophysiological study-induced malignant ventricular arrhythmias data were analyzed. A total of 45 patients (60.2±11.29 years, 57.8% males) were included. The mean HV interval was 58.37 ms±10.68; 22.2% of the studied population presented an HV interval of ≥70 ms; and malignant ventricular arrhythmias were induced in 57.8% patients. The use of beta-blockers and amiodarone (p=0.002 and 0.036, respectively), NYHA functional class≥II (p=0.013), wide QRS (p=0.047), increased HV interval (p=0.02), Rassi score >6.5 (p=0.003), and reduced left ventricular ejection fraction (p=0.031) were associated with increased risk of inducible malignant ventricular arrhythmias. More than half of the patients with Chagas disease, syncope, and cardiac conduction disorder have inducible malignant ventricular arrhythmias. Prolonged HV interval was observed in only 20% of population. Wide QRS, prolonged HV, reduced ejection fraction, and higher Rassi score were associated with increased risk of malignant ventricular arrhythmias.

Corporate governance and return on assets in mining industry companies: The developing market study

Differences in interests lead to conflict between managers with owners of capital because managers do not always align interests with the interests of company owners (Jensen & Meckling, 1976). Corporate governance has a very important role in increasing various growths, one of which is the growth of the company’s finances. In the application of corporate governance, it takes several parties who can bridge corporate governance to be applied in the company. The board of commissioners is the core of governance that is tasked with ensuring the implementation of the company’s strategy, supervising management, and requiring accountability. The purpose of this study was to find out what important parties in the company had a significant impact on the company’s finances as measured through the return on assets (ROA) of mining companies. This study uses secondary data collected from financial statements and annual reports from mining companies listed on the Indonesia Stock Exchange (IDX) that can be accessed regularly. In this study, data analysis to test hypotheses was multiple linear regression analysis. The analysis of multiple linear regression data measures the interval or ratio data to know whether the free variables studied have a good correlation. The results of the study show that all parties who have an important role in bridging corporate governance such as the board of commissioners, independent commissioners, board of directors, and audit committee, have no significant influence on the growth of ROA in the company.

Inexact multi-attribute decision analysis of groundwater remediation strategies with inputs of interval data

This study introduced an inexact interval-based multi-attribute decision analysis (IMADA) method with AHP for identifying the compromised groundwater remediation strategies in different periods. This IMADA method has the following advantages: (1) provides a systematic and quantitative analysis procedure for comparing potential pumping alternatives under four remediation duration; (2) reflects the priorities of the project based on the points of view of different decision makers; (3) compromises among possibly tangible and intangible attributes according to a final ranking of pumping alternatives. The method is applied to a contaminated aquifer located in southeastern China, where a period of remediation action should be taken. Ten influential attributes were considered and 50 alternative remediation strategies were generated. Results from the case study indicate that action 48 is the optical remediation strategy under 5-year period, action 5 in 10-year, action 33 during 15-year period and action 26 in 20-year.

Study on the spatial variation of sensitivity of soil nutrient system in Xinjiang, China

<abstract> <p>Previous studies have explored the long time series and large-scale cultivated land nutrient sensitivity and its spatial differentiation characteristics in arid zones from human activities in the context of climate change. This study is based on 10-year interval data on soil nutrient content of cultivated land in the oasis in Xinjiang, China, cultivated land use intensity (LUI) and climate data sets. Using sensitivity and GIS analysis methods, this paper studies soil nutrient sensitivities and their spatial distribution patterns in the context of LUI and climate change. The results showed significant response differences and spatial heterogeneity regarding the sensitivity of soil nutrient systems to LUI and climate change. Among them, soil nutrients were the most sensitive to temperature changes, followed by LUI, while precipitation was the weakest. Soil nutrient sensitivity showed a decreasing spatial distribution pattern from the northeast to the southwest. The soil nutrient system had a strong adaptability to LUI and climate change. However, there were differences in different sensitivity states. These results provide scientific guidance for the spatial selection and implementation of soil fertility enhancement and land remediation projects in similar arid areas.</p> </abstract>

On the problem of calculating steady state modes of electric power systems under conditions of interval data uncertainty

Currently, there are several approaches for dealing with uncertain (inaccurate) data. The main ones are methods of probabilistic analysis, fuzzy set theory and interval analysis. In this paper, we consider the problem of calculating the parameters of steady-state modes of electric power systems with interval uncertainty of the initial data. The main reasons and the relevance of the use of interval methods for calculating the parameters of steady-state modes of networks of electrical systems are described. First, an interval calculation model is formulated, and then some interval iterative methods for solving nonlinear nodal equations of electrical networks are studied. Algorithms for the interval methods of Gauss-Seidel and Newton-Raphson are proposed for solving nonlinear nodal equations of steady state electrical networks. To demonstrate the level of efficiency of the developed algorithms, several test calculations were carried out with interval parameters formed through the middle and radius of the interval. The results of numerical calculations using these methods show that the Newton-Raphson method is superior to the Gauss-Seidel method in terms of the number of iterations and optimality (with a smaller width) of interval solutions.

Using slacks-based model to solve inverse DEA with integer intervals for input estimation

This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of DMU_o increases from Y_o to beta _o, such the new DMU is given by (alpha _o^*,beta ) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables.

STOCHASTIC TRAFFIC DEMAND PROFILE

Traffic surveys routinely estimate the profile of traffic demand in a certain road section, showing the expected evolution of the demand over a workday or weekend. However, the actual demand fluctuates around this value. That can lead to brief excess of the capacity at the moment of high demand and consequent congestion due to the capacity drop. This type of traffic demand variability has not yet been properly studied despite the fact it can play significant role in traffic modelling and engineering applications. This paper presents results of analysis of demand variability in five-minute aggregation intervals. The results do not clearly show a single random distribution that would accurately model the demand variability. Normal, lognormal and gamma distributions all show reasonably well fit to the data for individual intervals. Based on count of best fits, the lognormal distribution seems best, but in most cases, the difference between the distributions is not statistically significant. There appears to be a pattern where certain distributions have better fit in different times of day and week. The regularity and magnitude of demand (e.g. morning peak hour) probably play a role in this, as well as the aggregation interval.

Rainwater Harvesting Practices and Its Effectiveness in Kathmandu Metropolitan City

Water scarcity has been a major problem of Kathmandu Metropolitan City (KMC). Different interventions are being attempted to solve this problem including the highly discussed Melamchi Drinking Water supply project. Thus, so rainwater harvesting (RWH) could be a promising approach to satisfy water to some extent. The study has aimed to assess the status of rainwater harvesting practices in KMC and to examine its effectiveness in overcoming the water shortage. A total of 244 households were surveyed covering 32 wards of KMC through random sampling method and semi structured questionnaire forms were laid for the data collection. The annual rainfall data of interval 30 years (1990-2019) of KMC, collected from department of Hydrology and Meteorology for trend analysis. Study revealed 58.2% of households are practicing RWH and among them 63.2% installed RWH system more than five years ago. About 63% of households are practicing roof top harvesting which is found to be more convenient in terms of cost and space. Strong positive correlation (R2=0.876, r=0.942) was observed among amount of water harvested and space occupied by RWH system and was statistically significant (P <0.05). Harvested water is found mainly used for household’s chores, flushing toilets and watering the garden. Majority (95.8%) of respondents did not prefer harvested water for drinking due to its poor water quality, high contamination and bad odor and taste. About 73.2% of the respondents decontaminate harvested water before using and filtration (63%) is found to be most common and effective method for decontamination. Despite of challenges like leakages of storages and gutters, about 87.3% of respondents are strongly satisfied with RWH system as it reduced the municipal water supply bill and provides excess water for the sanitation. Furthermore, the trend analysis showed increment of rainfall in the area by 1.21 mm per annum. Study regarding governmental incentives for the installation of RWH system, availability and accessibility of quality products, training on installation and sanitary management of RWH system would help to shed further light in the aspects of RWH.

Are Infinite-Failure NHPP-Based Software Reliability Models Useful?

In the literature, infinite-failure software reliability models (SRMs), such as Musa-Okumoto SRM (1984), have been demonstrated to be effective in quantitatively characterizing software testing processes and assessing software reliability. This paper primarily focuses on the infinite-failure (type-II) non-homogeneous Poisson process (NHPP)-based SRMs and evaluates the performances of these SRMs comprehensively by comparing with the existing finite-failure (type-I) NHPP-based SRMs. In more specific terms, to describe the software fault-detection time distribution, we postulate 11 representative probability distribution functions that can be categorized into the generalized exponential distribution family and the extreme-value distribution family. Then, we compare the goodness-of-fit and predictive performances with the associated 11 type-I and type-II NHPP-based SRMs. In numerical experiments, we analyze software fault-count data, collected from 16 actual development projects, which are commonly known in the software industry as fault-count time-domain data and fault-count time-interval data (group data). The maximum likelihood method is utilized to estimate the model parameters in both NHPP-based SRMs. In a comparison of the type-I with the type-II, it is shown that the type-II NHPP-based SRMs could exhibit better predictive performance than the existing type-I NHPP-based SRMs, especially in the early stage of software testing.

Quantile regression with interval-censored data in questionnaire-based studies

Interval-censored data can arise in questionnaire-based studies when the respondent gives an answer in the form of an interval without having pre-specified ranges. Such data are called self-selected interval data. In this case, the assumption of independent censoring is not fulfilled, and therefore the ordinary methods for interval-censored data are not suitable. This paper explores a quantile regression model for self-selected interval data and suggests an estimator based on estimating equations. The consistency of the estimator is shown. Bootstrap procedures for constructing confidence intervals are considered. A simulation study indicates satisfactory performance of the proposed methods. An application to data concerning price estimates is presented.

Electric energy consumption predictions for residential buildings: Impact of data-driven model and temporal resolution on prediction accuracy

This study aims to investigate the measurement parameters for predicting the electric energy consumption of residential buildings using a data-driven model. Herein, the temporal resolution of data and algorithms that can improve prediction accuracy are comparatively investigated. For the investigation, the time units of the data collected from the monitoring system of an actual residential building are set as 10 min and 1 h. Further, algorithms such as multiple linear regression (MLR), multilayer perceptron (MLP), support vector machine (SVM), and random forest (RF) are employed to predict the electric energy consumption of the building. The parameters of the data collection include electric energy consumption based on the usage type, occupancy information, and indoor environmental information. The model is validated using a K-fold technique, and the prediction accuracy is compared using R 2 and the t -value. Analyses using seven input variables reveal that the prediction accuracy for the 1 h interval data is better than that for the 10 min interval data, based on the temporal resolution of the data. In addition, the results of the algorithms reveal that the prediction accuracy is the highest when the MLR algorithm is used, followed by those when using the RF, MLP, and SVM algorithms. A relatively simple statistical method and low-resolution data rather than a complex machine learning algorithm or high-resolution data achieved the best prediction accuracy. These results are expected to facilitate high-accuracy predictions of the electric energy consumption of residential buildings. • Predictions of residential energy consumption were studied using a data-driven model. • Energy consumption information was measured and collected in a residential building. • The collected data were usage type, occupancy, and indoor environmental information. • The prediction accuracy is compared based on temporal resolutions and algorithms. • These results will be useful for the energy management of residential buildings.

Predicting Volatility Based on Interval Regression Models

Considering the inferior volatility tracking capability of the point-data-based models, we propose using the more informative price interval data and building interval regression models for volatility forecasting. To characterize the heterogeneity of the market and the nonlinearity of volatility, we incorporated the heterogeneous autoregressive structure and the Markov regime switching structure in the benchmark interval regression model, respectively, and thus propose three extended models. Our empirical examination on S&P 500 index shows that: (1) the proposed interval regression models significantly improve the volatility prediction accuracy compared to the point-data-based GARCH model. (2) Incorporating the heterogeneous structure significantly improves the volatility prediction accuracy, and the corresponding models significantly outperform the range-based ECARR model. (3) Incorporating the Markov regime switching structure improves the prediction performance, and the improvement is significant when the heterogeneous structure is characterized. The above results are robust under different market conditions, including the extremely volatile periods.

Development of an epileptic seizure prediction algorithm using R–R intervals with self-attentive autoencoder

Epilepsy is a neurological disorder that may affect the autonomic nervous system (ANS) from 15 to 20 min before seizure onset, and disturbances of ANS affect R–R intervals (RRI) on an electrocardiogram (ECG). This study aims to develop a machine learning algorithm for predicting focal epileptic seizures by monitoring R–R interval (RRI) data in real time. The developed algorithm adopts a self-attentive autoencoder (SA-AE), which is a neural network for time-series data. The results of applying the developed seizure prediction algorithm to clinical data demonstrated that it functioned well in most patients; however, false positives (FPs) occurred in specific participants. In a future work, we will investigate the causes of FPs and optimize the developing seizure prediction algorithm to further improve performance using newly added clinical data.

A Novel Adaptive Noise Elimination Algorithm in Long RR Interval Sequences for Heart Rate Variability Analysis.

As heart rate variability (HRV) studies become more and more prevalent in clinical practice, one of the most common and significant causes of errors is associated with distorted RR interval (RRI) data acquisition. The nature of such artifacts can be both mechanical as well as software based. Various currently used noise elimination in RRI sequences methods use filtering algorithms that eliminate artifacts without taking into account the fact that the whole RRI sequence time cannot be shortened or lengthened. Keeping that in mind, we aimed to develop an artifacts elimination algorithm suited to long-term (hours or days) sequences that does not affect the overall structure of the RRI sequence and does not alter the duration of data registration. An original adaptive smart time series step-by-step analysis and statistical verification methods were used. The adaptive algorithm was designed to maximize the reconstruction of the heart-rate structure and is suitable for use, especially in polygraphy. The authors submit the scheme and program for use.

Trajectory Prediction of Marine Moving Target Using Deep Neural Networks with Trajectory Data

The position prediction of marine moving targets based on historical trajectories is an important assistance procedure for marine reconnaissance and surveillance. Limited by satellite access period, space-based historic trajectory data have sparse and uneven intervals. However, most current time-series prediction methods require uniform time intervals. For non-uniform time series data, common processing methods first use the interpolation algorithm to fit historical data, and then carry out predictions based on equal interval data after the uniform sample. The disadvantage is that the accuracy of the interpolation data will limit the prediction accuracy. In addition, the time-series prediction methods represented by the grey model (GM) and autoregressive model (ARM) can only deal with equal-interval time prediction, in which it is hard to satisfy the prediction demand of non-equidistant time. Aiming at the limitations of most time series prediction methods and meeting the requirement of long-term variable duration prediction, a novel trajectory prediction method for sparse and non-uniform time series data based on deep neural networks is proposed. Firstly, to maximize the mining of the original data features, the moving behavior features are extracted from the raw historical track data by calculating the information of position, velocity, and position change for feature extension. Then, because of the temporal coherence of the track data, and inspired by the design idea of local correlation of the convolutional neural network (CNN), the CNN model is used to excavate the navigation rules to achieve position prediction. Finally, training of the network model is accomplished based on historical track samples. The experiments are carried out based on the space-borne automatic identification system (AIS) observation data. Experimental results illustrate that the method behaves better than other methods with the superiority of lower requirements for sampling, stronger adaptability to data characteristics, and higher forecasting accuracy for long-term prediction. When applied to the satellite search of marine moving targets, the track prediction has the potential to reduce the uncertainty of target location and guide satellite searching missions, thereby significantly improving the searching efficiency of targets.

A model for bimodal rates and proportions

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution, such as bimodality, real moments, entropies and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality.