Confidence Bands Research Articles

Generalized varying-coefficient additive model for locally stationary time series

ABSTRACT Recently, the varying-coefficient additive model (VCAM) has received much attention due to its flexibility and interpretability. In this paper, we consider its generalized form, called a generalized varying-coefficient additive model (GVCAM), which can model discrete and continuous responses for locally stationary covariates. Specifically, the conditional mean function is specified via a link function g and a nonparametric part given by a VCAM. We develop a pilot-estimation-based local linear maximum likelihood estimator (PEB-LLE) to approximate the univariate component function. We also show the proposed estimators are oracle efficient and present the pointwise asymptotic distribution as well as simultaneous confidence bands. Simulation studies investigating the finite-sample performance of the proposed methodology are considered, and a real data application illustrating our method is also given.

Empirical Likelihood-Based Inference for Functional Means with Application to Wearable Device Data

AbstractThis paper develops a nonparametric inference framework that is applicable to occupation time curves derived from wearable device data. These curves consider all activity levels within the range of device readings, which is preferable to the practice of classifying activity into discrete categories. Motivated by certain features of these curves, we introduce a powerful likelihood ratio approach to construct confidence bands and compare functional means. Notably, our approach allows discontinuities in the functional covariances while accommodating discretization of the observed trajectories. A simulation study shows that the proposed procedures outperform competing functional data procedures. We illustrate the proposed methods using wearable device data from an NHANES study.

Data-Driven Ranking and Selection Under Input Uncertainty

In many applications, input data are collected frequently to update the simulation model of the system, whereas simulation is run to compare different designs/strategies to identify the best one with a high confidence. In “Data-Driven Ranking and Selection Under Input Uncertainty,” Wu, Wang, and Zhou consider such a simulation-based ranking and selection (R&S) problem, in which the input distribution is estimated and updated with input data arriving in batches over time. Unlike most existing works of R&S that conduct simulation under a fixed distribution, in this data-driven setting, simulation outputs are generated under different input distributions over time. A moving average estimator is introduced to aggregate simulation outputs generated under heterogenous distributions. Then, two sequential elimination procedures are devised by establishing exact and asymptotic confidence bands for the estimator. The efficiency of the procedures can be further boosted by incorporating the “indifference zone” idea and optimizing the “drop rate” parameter of the moving average estimator.

Data Recovery of the Sea of Azov Salinity Fields Using Regression Analysis Between In Situ Data and Regional Satellite Products

This study proposes a method for obtaining information on the salinity of the Sea of Azov, based on the use of contact and remote sensing data. The approach to the salinity fields recovery is based on obtaining generalized regression equations relating in situ archival data with regional biooptical products obtained from standard level-2 MODIS products. This analysis showed the possibility of using various approaches to obtain generalized empirical (regression) equations for the spring and summer seasons, the differences in which are ~10 %. The results of the recovered salinity values were verified using in situ data. It was found that the plots of the average values of the recovered salinity are in the region of 95 % of the confidence bands of the modern long-term average trends for 1986–2018 and 2000–2018. The possibility of using the results of the proposed method in the construction of spatial maps of the Azov Sea salinity, synchronized in time with satellite scenes, is shown.

Experimental study of the shear strength criterion of rock structural plane based on three-dimensional surface description

Abstract The failure of rock mass is mainly due to the failure of the structural plane, which is an important factor to reduce the mechanical properties and stability of rock mass. The shear strength of rock mass is one of the parameters for the stability calculation of large-scale rock mass engineering. The shear strength of a rock structural plane is strongly influenced by surface morphology. Considerable research has been conducted regarding the correlation between two-dimensional structural plane morphology and shear strength. However, quantitative research on three-dimensional (3D) morphology is relatively limited. In this study, 3D printing technology was used to create molds. Using cement and sand as the main materials, additives such as early strength and water-reducing agents were added, and test samples of irregular surface topography were created. The 3D roughness was quantified by formula calculation. Using a ZScanner® 800 hand-held 3D laser scanner to perform scanning on the structural surface, the parameter curve was analysed by generating 3D coordinate information and a 3D image of the fracture surface, and the quantitative parameter M p 3 D {M}_{\text{p}}^{3\text{D}} describing the 3D morphology of the structural surface was constructed. The change rule of R p 3 D {R}_{\text{p}}^{3\text{D}} and joint roughness coefficient (JRC) were analysed under different scanning resolutions, Δ(r), the scanning precision was suggested, and the functional relationship between JRC and M p 3 D {M}_{\text{p}}^{3\text{D}} was established. Finally, a formula for shear strength parameters considering the 3D characteristics of a structural plane surface was established. The model validation results show that the experimental data were within the 95% confidence band of the model curve, the average error of the shear strength was 10.4%, the errors of friction angle and cohesion, C, were 3.4 and 9.4%, and the reliability was fine.

Forecasting low‐frequency macroeconomic events with high‐frequency data

SummaryHigh‐frequency financial and economic indicators are usually time‐aggregated before computing forecasts of macroeconomic events, such as recessions. We propose a mixed‐frequency alternative that delivers high‐frequency probability forecasts (including their confidence bands) for low‐frequency events. The new approach is compared with single‐frequency alternatives using loss functions for rare‐event forecasting. We find (i) the weekly‐sampled term spread improves over the monthly‐sampled to predict NBER recessions, (ii) the predictive content of financial variables is supplementary to economic activity for forecasts of vulnerability events, and (iii) a weekly activity index can date the 2020 business cycle peak in real‐time using a mixed‐frequency filtering.

"PSEUDOCOMPENSATION": ITS DEFINITION AND GENESIS

"PSEUDOCOMPENSATION": ITS DEFINITION AND GENESIS

Electrical Breakdown of Oil-Impregnated Pressboard under AC and DC Voltages Ramp

In this work, we present an experimental study on electrical breakdown, also called dielectric failure on a material widely used as insulation in oil transformers and other equipment. This material is pressboard paper impregnated with insulating oil. The breakdown tests are carried out under three types of voltage and for several voltage rise speeds. Dielectric breakdown is a random phenomenon, many tests are carried out on a large number of samples and the results obtained have been subjected to statistical processing. The material is cut into square plates of 7.5 cm in length from a set of plates 2 m² in length and 500 µm in thickness. Prior to the tests, the samples were conditioned in a desiccator with silicone gel for at least 24 hours in order to eliminate any presence of moisture. Then they were impregnated with Borak22 insulating oil for at least one week. The tests consist of placing the sample concerned between two cylindrical bronze electrodes and applying a voltage ramp at constant speed until breakdown. After failure, the value of the breakdown voltage is taken. These tests are carried out in the laboratory at room temperature. However, we have tried to reproduce the same conditions for all the tests. These various tests relate to the effect of the form and the rate of rise of the applied voltage on the dielectric strength of the pressboard paper impregnated with Borak22 insulating oil. Two measuring devices were used, and the tests were carried out under three voltage forms: sinusoidal alternating current, continuous positive polarity, and continuous negative polarity, and at eight different voltage ramp speeds: 0,69; 1,07; 1,4; 1,89; 2,38; 2,94; 3,28 and 4,17 kV/s. For each measurement point, 35 samples of pressboard paper are used and tested. A total of 840 results were obtained and processed using the two-parameter Weibull statistical model. In order to validate this model, these results are subjected to a Kolmogorov-Smirnov adequacy test and are framed by 95% confidence bands. The maximum likelihood method is used for the estimation of the Weibull parameters and the smoothing of the experimental points. The results of the statistical tests on the breakdown voltage measurement points obtained confirm the use of the two-parameter Weibull model. The evolution of the nominal breakdown voltage as a function of the voltage ramp of the three forms of applied voltage gives three properties of the same form, which is akin to the letter 'S'. The breakdown voltage first increases linearly for low speeds, then increases and takes an exponential form for medium speeds, then tends towards a certain saturation for high speeds. The breakdown voltage under the DC voltage ramp is higher than the voltage obtained for the AC voltage ramp and are higher under negative polarity voltage than those under positive polarity voltage.

Convergence rate of plugin estimates for functional parameters with applications to locally-stationary time-series

Some distribution parameter estimates depend on nuisance parameters, and it is a common practice to plug in their estimates. The convergence properties of the resulting estimate are of interest. We consider the case where both estimators – the one plugged in, and its recipient – are random quantities, while literature covers mostly plugin to a deterministic function. We present a way of computing this final convergence rate, based on the convergence rate of a nonrandom, but perturbed quantity plugged in. The theoretical result is applied to the construction of simultaneous confidence band for auto-correlation functions of a locally-stationary time series.

Ferritin Increase in Hemochromatosis Subjects After Discontinuing Their Regular Maintenance Treatment: A Longitudinal Analysis Performed During the COVID-19 Imposed Hospital Lockdown.

Ferritin Increase in Hemochromatosis Subjects After Discontinuing Their Regular Maintenance Treatment: A Longitudinal Analysis Performed During the COVID-19 Imposed Hospital Lockdown.

Simultaneous confidence bands and global inferences for extended partially linear single-index models

Substantial efforts have been made for the popular semiparametric single-index models in the last two decades. Extended partially linear single-index models as generalized single-index semiparametric models effectively reduce the problem of model misspecification by allowing the data to automatically choose the principal linear component and the principal nonlinear component. In this paper, we construct an oracle-efficient simultaneous confidence band as a global inference tool for the extended partially linear single-index models. Specifically, we apply a LASSO penalized local linear smoothing method to estimate the coefficient parameters and conduct variable selection to avoid model overfitting caused by the two appearances of covariates. It is shown that the local linear estimator for the nonparametric link function by employing the penalized coefficient estimates is oracle-efficient in the sense that it is uniformly as efficient as the ideal one obtained by utilizing the true coefficient parameters. Then by applying the oracle efficiency and the extreme value distribution theory of the local linear regression, an asymptotically accurate simultaneous confidence band for the nonparametric link function in the extended partially linear single-index models is established. Simulation experiments with commonly encountered sample sizes corroborate our theoretical findings. The proposed method is applied to analyze two engineering datasets: motor trend car road tests dataset and concrete slump tests dataset.

Confidence bands in survival analysis

BackgroundProviding estimates of uncertainty for statistical quantities is important for statistical inference. When the statistical quantity of interest is a survival curve, which is a function over time, the appropriate type of uncertainty estimate is a confidence band constructed to account for the correlation between points on the curve, we will call this a simultaneous confidence band. This, however, is not the type of confidence band provided in standard software, which is constructed by joining the confidence intervals at given time points.MethodsWe show that this type of band does not have desirable joint/simultaneous coverage properties in comparison to simultaneous bands.ResultsThere are different ways of constructing simultaneous confidence bands, and we find that bands based on the likelihood ratio appear to have the most desirable properties. Although there is no standard software available in the three major statistical packages to compute likelihood-based simultaneous bands, we summarise and give code to use available statistical software to construct other simultaneous forms of bands, which we illustrate using a study of colon cancer.ConclusionsThere is a need for more user-friendly statistical software to compute simultaneous confidence bands using the available methods.

Estimating sizes of type-2 AGN narrow-line regions from multiple survey spectra – a demonstration

ABSTRACT In the Letter, an interesting method is proposed to estimate size of narrow emission-lines regions (NLRs) of a type-2 AGN SDSS J083823.91 + 490241.1 (=SDSS J0838) at a redshift of 0.101, by comparing spectroscopic properties through the SDSS fibre (MJD = 51873) (diameter of 3 arcsec) and through the eBOSS fibre (MJD = 55277) (diameter of 2 arcsec). After subtractions of ppxf method determined host galaxy contributions, the narrow emission lines of SDSS J0838 in the SDSS spectrum and in the eBOSS spectrum can be well measured by Gaussian functions, leading more than 90 per cent of [O iii] emissions to be covered by the eBOSS fibre with diameter of 2 arcsec. Meanwhile, both none broad emission components and none-variabilities of ZTF 3 yr-long g-/r-band light curves can be applied to confirm SDSS J0838 as a type-2 AGN, indicating few orientation effects on the projected NLRs size in SDSS J0838. Therefore, upper limit about 1 arcsec (2250 pc) of the NLRs size can be reasonably accepted in SDSS J0838. Combining with the intrinsic reddening corrected [O iii] line luminosity, the upper limit of NLRs size in SDSS J0838 well lies within the 99.9999 per cent confidence bands of the R-L empirical relation for NLRs in AGN.

The Neutrophil-to-Lymphocyte Ratio and the Platelet-to-Lymphocyte Ratio as Predictors of Mortality in Older Adults Hospitalized with COVID-19 in Peru.

Background The prognostic value of the neutrophil-lymphocyte ratio (NLR) and platelet-lymphocyte ratio (PLR) in patients with COVID-19 is rarely described in older adults. We aimed to estimate the prognostic value of NLR and PLR, determining the mortality of adults over 60 years of age hospitalized for COVID-19 in three hospitals in Peru from March to May 2020. Methods We performed a secondary analysis of data from a retrospective cohort carried out in Lambayeque, Peru, from March 18 to May 13, 2020. Older adults hospitalized for COVID-19 were included. The outcome variable was in-hospital mortality by all causes, while the exposure variable was the NLR and PLR (categorized in tertiles and numerically, performing a logarithmic transformation). We included sociodemographic variables, comorbidities, vital functions, laboratory markers, and treatment received during hospital stay. We evaluated the association between NLR and PLR using the hazard ratio (HR) in a Cox regression model. We estimated HR with their respective 95% confidence intervals (95% CI). We estimated cumulative/dynamic time-dependent ROC curves and reported area under the curve ROC (AUC-ROC) for 15-, 30-, and 60-day mortality with their respective simultaneous confidence intervals (confidence bands (CB)). Also, we estimated an optimal cut-off point based on the maximally selected rank statistics. Results A total of 262 hospitalized older adults were analyzed, 71.8% (n = 188) of whom were male with a median age of 70 years (interquartile range: 65-78). The mean NLR and PLR were 16.8 (95% CI: 14.9-18.7; SD: 15.5) and 50.3 (95% CI: 44.6-55.9; SD: 46.3), respectively. The mortality rate was 68.7% (95% CI: 62.7-74.3). The adjusted Cox regression analysis showed that the high NLR (adjusted HR (aHR) = 2.12; 95% CI: 1.43-3.14) and PLR (aHR = 1.90; 95% CI: 1.30-2.79) tertiles were associated with a higher risk of mortality. The maximum AUC-ROC values at 60 days of follow-up for NLR and PLR were 0.713 (95%CB: 0.627-0.800) and 0.697 (95%CB: 0.583-0.754), respectively. Conclusions The NLR and PLR are predictors of higher risk of mortality, and these results suggest that both could be reliable and practical markers for the identification of older adults at high risk of mortality by COVID-19. NLR and PLR have prognostic value, with an AUC greater than 0.5; however, by themselves, they are weak prognostic markers. It is important to carry out future studies incorporating these two markers into preexisting models or designing new ones considering them.

SIMULTANEOUS CONFIDENCE BANDS FOR CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL

Conditional value-at-risk (CVaR) and conditional expected shortfall (CES) are widely adopted risk measures which help monitor potential tail risk while adapting to evolving market information. In this paper, we propose an approach to constructing simultaneous confidence bands (SCBs) for tail risk as measured by CVaR and CES, with the confidence bands uniformly valid for a set of tail levels. We consider one-sided tail risk (downside or upside tail risk) as well as relative tail risk (the ratio of upside to downside tail risk). A general class of location-scale models with heavy-tailed innovations is employed to filter out the return dynamics. Then, CVaR and CES are estimated with the aid of extreme value theory. In the asymptotic theory, we consider two scenarios: (i) the extreme scenario that allows for extrapolation beyond the range of the available data and (ii) the intermediate scenario that works exclusively in the case where the available data are adequate relative to the tail level. For finite-sample implementation, we propose a novel bootstrap procedure to circumvent the slow convergence rates of the SCBs as well as infeasibility of approximating the limiting distributions. A series of Monte Carlo simulations confirm that our approach works well in finite samples.

Effects of digital processing on repeatability assessment of a multiple reaction monitoring liquid chromatography-tandem mass spectrometry system by ISO 11843-7.

ISO 11843 part 7 (ISO 11843-7) can provide a standard deviation (SD) of area measurements of a target peak through the stochastic behaviors of instrumental noises. The purpose of this study is to demonstrate that ISO 11843-7 can be applied to assess repeatability in an isocratic liquid chromatography-tandem mass spectrometry (LC-MS/MS) system without repetitive measurements. The relative standard deviation (RSD) of the peak area of ergosterol picolinyl ester, which was used as an example, on a multiple reaction monitoring (MRM) chromatogram was determined by ISO 11843-7. The RSD by ISO 11843-7 (N = 1) was within a 95% confidence band of the RSD by repetitive measurements (N = 6). Moreover, the effects of digital smoothing, such as moving average, were also examined on the repeatability assessment in LC-MS/MS by ISO 11843-7. From the results of the comparisons of the RSDs obtained by ISO 11843-7 and the repetitive measurements, it was shown that suitable RSDs of the peak area were obtained from the smoothed MRM chromatograms by the moving average for narrow data point windows (e.g., one-sixth of the peak width). In conclusion, the utility of repeatability assessment based on ISO 11843-7 has been expanded for the validation of an LC-MS/MS system.

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.

Confidence bands and hypothesis tests for hit enrichment curves

In virtual screening for drug discovery, hit enrichment curves are widely used to assess the performance of ranking algorithms with regard to their ability to identify early enrichment. Unfortunately, researchers almost never consider the uncertainty associated with estimating such curves before declaring differences between performance of competing algorithms. Uncertainty is often large because the testing fractions of interest to researchers are small. Appropriate inference is complicated by two sources of correlation that are often overlooked: correlation across different testing fractions within a single algorithm, and correlation between competing algorithms. Additionally, researchers are often interested in making comparisons along the entire curve, not only at a few testing fractions. We develop inferential procedures to address both the needs of those interested in a few testing fractions, as well as those interested in the entire curve. For the former, four hypothesis testing and (pointwise) confidence intervals are investigated, and a newly developed EmProc approach is found to be most effective. For inference along entire curves, EmProc-based confidence bands are recommended for simultaneous coverage and minimal width. While we focus on the hit enrichment curve, this work is also appropriate for lift curves that are used throughout the machine learning community. Our inferential procedures trivially extend to enrichment factors, as well.

Functional delta residuals and applications to simultaneous confidence bands of moment based statistics

Given a functional central limit (fCLT) for an estimator and a parameter transformation, we construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the limit process of the functional delta method. An explicit construction of these residuals for transformations of moment-based estimators and a multiplier bootstrap fCLT for the resulting functional delta residuals are proven. The latter is used to consistently estimate the quantiles of the maximum of the limit process of the functional delta method in order to construct asymptotically valid simultaneous confidence bands for the transformed functional parameters. Performance of the coverage rate of the developed construction, applied to functional versions of Cohen’s d, skewness and kurtosis, is illustrated in simulations and their application to test Gaussianity is discussed.

Interval Prediction of Building Foundation Settlement Using Kernel Extreme Learning Machine

Dynamic building foundation settlement subsidence threatens urban businesses and residential communities. In the temporal domain, building foundation settlement is often dynamic and requires real-time monitoring. Accurate quantification of the uncertainty of foundation settlement in the near future is essential to advanced risk management for buildings. Traditional models for predicting foundation settlement mostly utilize the point estimates approach, which provides a single value that can be close or distant from the actual one. However, such an estimation fails to quantify estimation uncertainties. The interval prediction, as an alternative, can provide a prediction interval for the ground settlement with high confidence bands. This study, proposes a lower upper bound estimation approach integrated with a kernel extreme learning machine to predict ground settlement levels with prediction intervals in the temporal domain. A revised objective function is proposed to further improve the interval prediction performance. In this study, the proposed method is compared to the artificial neural network and classical extreme learning machine. Building settlement data collected from Fuxing City, Liaoning Province in China was used to validate the proposed approach. The comparative results show that the proposed approach can construct superior prediction intervals for foundation settlement.