Accurate Error Estimates Research Articles

Estimating standard errors for life expectancies based on complex survey data with mortality follow‐up: A case study using the National Health Interview Survey Linked Mortality Files

Life expectancy is an important measure for health research and policymaking. Linking individual survey records to mortality data can overcome limitations in vital statistics data used to examine differential mortality by permitting the construction of death rates based on information collected from respondents at the time of interview and facilitating estimation of life expectancies for subgroups of interest. However, use of complex survey data linked to mortality data can complicate the estimation of standard errors. This paper presents a case study of approaches to variance estimation for life expectancies based on life tables, using the National Health Interview Survey Linked Mortality Files. The approaches considered include application of Chiang's traditional method, which is straightforward but does not account for the complex design features of the data; balanced repeated replication (BRR), which is more complicated but accounts more fully for the design features; and compromise, 'hybrid' approaches, which can be less difficult to implement than BRR but still account partially for the design features. Two tentative conclusions are drawn. First, it is important to account for the effects of the complex sample design, at least within life-table age intervals. Second, accounting for the effects within age intervals but not across age intervals, as is done by the hybrid methods, can yield reasonably accurate estimates of standard errors, especially for subgroups of interest with more homogeneous characteristics among their members.

Contouring controller design based on iterative contour error estimation for three-dimensional machining

Recently, there has been a growth of interest in high precision machining in multi-axis feed drive systems, subjected to problems such as friction, cutting force and incompatibility of individual driving axis dynamics. To guarantee high precision machining in modern computer numerical controlled (CNC) machines, CNC's controllers do its control efforts to reduce contour error. One of the common approaches is to design a controller based on the estimation of contour error in real time. However, for complex contours with severe curvatures, there is a lack of effective algorithms to calculate contour errors accurately. To address this problem, this paper proposes an accurate contour error estimation procedure for three-dimensional machining tasks. The proposed method is based on an iterative estimation of the instantaneous curvature of the reference trajectory and coordinates transformation approach, and hence, it is effective for complex reference trajectories with high curvatures. In addition, contour error controller is presented to reduce the estimated contour error. The feasibility and superiority of the proposed model as well as contour error controller are demonstrated through experimental system using a desk-top three-axis CNC machine.

Initial orientation of inertial navigation system realized through nonlinear modeling and filtering

Alignment is the process whereby the orientation of the axes of an inertial navigation system is determined with respect to the reference system. In this paper, the initial alignment error equations of the strapdown inertial navigation system (SINS) with large initial azimuth error have been derived with inclusion of nonlinear characteristics. Simulations have been carried out to validate and corroborate the stationary alignment case employing a strapdown inertial measurement unit (SIMU). A performance comparison between the extended Kalman filter (EKF), the unscented Kalman filter (UKF) and the second-order divided difference filter (DDF2) demonstrate that the accuracy of attitude error estimation using the DDF2 is better than that of using the EKF or the UKF.

A simple estimator for stress errors dedicated to large elastic finite element simulations

PurposeThis paper aims to deal with the verification of local quantities of interest obtained through linear elastic finite element analysis. A technique is presented for determining the most accurate error estimation. This technique enables one to address industrial‐size problems while keeping computing costs reasonable.Design/methodology/approachThe concept of error in constitutive relation is used to assess the quality of the finite element solution. The key issue is the construction of admissible fields. The objective is to show that it is possible to build admissible fields using a new method. These fields are obtained by using a high‐quality construction over a limited zone while the construction is less refined and less expensive elsewhere.FindingsNumerical tests are presented in order to illustrate a very satisfying presented methodology. It shows clearly how to take advantage of the method to treat large examples. They clearly show the interest of this new method to treat large examples.Originality/valueThe paper demonstrates clearly that verification of large finite element problem must have dedicated methods in order to be applicable.

The Effect of Feedback Teacher-Determined Different Procedures on Error Estimation Accuracy in Non Athlete Students

Although many studies being done for indentifying different feedback presentation procedures with positive effect on learning, but yet there are great numbers of questions regarding to the best possible procedure for presenting feedback to enhance learning remained to be considered. The aim of this study was investigate comparison different procedures in teacher-determined feedback on improve capability of error estimation accuracy in non athlete students. The present research is semi-experimental and is performed by participation in four stages as pre-test, acquisition, retention and transfer. The research design is as pre-test - post-test with 3 experimental groups. The Participants of this research consisted of 36 non-athlete students’ volunteers. Measuring apparatus is a manual dynamometer. According to the research results, no significant statistical difference between 3 teacher-determined feedback groups in terms of error estimation accuracy variable of force production in retention and transfer phases, and all these 3 manipulating result in improvement of error estimation accuracy. These researches results show that Choosing suitable methods and presenting teacher-determined feedback added with decreased frequency, in addition to led to improve error estimation accuracy and efficient learning, is also time consuming.

The high-accuracy ionosphere correcting algorithm for GNSS signals based on kalman filter

A filter-based algorithm for estimating the ionosphere error of the GNSS signals in the differential system is proposed in the paper. Based on the slow-varying characteristic of the ionosphere delay, the historical ionosphere delay data is involved in the algorithm. The measurement model is constructed according to the Grid Interpolation Model (GIM).The relevant analysis is conducted by the simulation and the corresponding results indicated that comparing with the traditional method, at least 60% promotion on the accuracy has been accomplished so that the algorithm in this paper can provide a more accurate estimation of the ionosphere error for GNSS signals.

Comparison of the effects of feedback frequency reduction procedures on capability of error detection & learning force production task

The main purpose of this research was the comparison of the effect of feedback Frequency Reduction procedures (bandwidth, summary and faded) on the performance improvement and error detection capability of force production task. The necessary data for the present research was gathered in 4 phases: pre-test, acquisition, retention and transfer. In pre-test phase, the subjects were supposed to produce a force equivalent to 20% of maximum force in a 10-trial block. The acquisition phase consisted of seven 10-trial blocks in which 30% of maximum force in were used as a target force. In retention phase in the next 24hours, production force procedure based on 30% of maximum force was used and in transfer phase, 40% of maximum force was used as the target force. For Data analysis, one-way analysis of variance and one-way analysis of co-variance in significant level P≤0.05 for spss-11.5 software were used. Results revealed that there was no significant statistical difference in accuracy variable, consistency variable, and error estimation accuracy variable of production force in acquisition, retention and transfer phase in three kinds of these manipulations, and they (manipulations) led to the improvement of learning and error detection capability.

G_wham—A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates

The Weighted Histogram Analysis Method (WHAM) is a standard technique used to compute potentials of mean force (PMFs) from a set of umbrella sampling simulations. Here, we present a new WHAM implementation, termed g_wham, which is distributed freely with the GROMACS molecular simulation suite. g_wham estimates statistical errors using the technique of bootstrap analysis. Three bootstrap methods are supported: (i) bootstrapping new trajectories based on the umbrella histograms, (ii) bootstrapping of complete histograms, and (iii) Bayesian bootstrapping of complete histograms, that is, bootstrapping via the assignment of random weights to the histograms. Because methods ii and iii consider only complete histograms as independent data points, these methods do not require the accurate calculation of autocorrelation times. We demonstrate that, given sufficient sampling, bootstrapping new trajectories allows for an accurate error estimate. In the presence of long autocorrelations, however, (Bayesian) bootstrapping of complete histograms yields a more reliable error estimate, whereas bootstrapping of new trajectories may underestimate the error. In addition, we emphasize that the incorporation of autocorrelations into WHAM reduces the bias from limited sampling, in particular, when computing periodic PMFs in inhomogeneous systems such as solvated lipid membranes or protein channels.

FAST AND OPTIMAL COSMIC MICROWAVE BACKGROUND LENSING USING STATISTICAL INTERPOLATION ON THE SPHERE

We describe a accurate and fast pixel-based statistical method to interpolate fields of arbitrary spin on the sphere. We call this method Fast and Lean Interpolation on the Sphere (FLINTS). The method predicts the optimal interpolated values based on the theory of isotropic Gaussian random fields and provides an accurate error estimate at no additional cost. We use this method to compute lensed Cosmic Microwave Background (CMB) maps precisely and quickly, achieving a relative precision of 0.02% at a HEALPix resolution of Nside=4096, for a bandlimit of l_max=4096 in the same time it takes to simulate the original, unlensed CMB map. The method is suitable for efficient, distributed memory parallelization. The power spectra of our lensed maps are accurate to better than 0.5% at l=3000 for the temperature, the E and B mode of the polarization. As expected theoretically, we demonstrate that, on realistic cases, this method is between two to three orders of magnitude more precise than other known interpolation methods for the same computational cost.

Tuning Support Vector Machines for Minimax and Neyman-Pearson Classification

This paper studies the training of support vector machine (SVM) classifiers with respect to the minimax and Neyman-Pearson criteria. In principle, these criteria can be optimized in a straightforward way using a cost-sensitive SVM. In practice, however, because these criteria require especially accurate error estimation, standard techniques for tuning SVM parameters, such as cross-validation, can lead to poor classifier performance. To address this issue, we first prove that the usual cost-sensitive SVM, here called the 2C-SVM, is equivalent to another formulation called the 2nu-SVM. We then exploit a characterization of the 2nu-SVM parameter space to develop a simple yet powerful approach to error estimation based on smoothing. In an extensive experimental study, we demonstrate that smoothing significantly improves the accuracy of cross-validation error estimates, leading to dramatic performance gains. Furthermore, we propose coordinate descent strategies that offer significant gains in computational efficiency, with little to no loss in performance.

Standard Errors of Parameter Estimates in the ETAS Model

Abstract Point process models such as the epidemic-type aftershock sequence (ETAS) model have been widely used to analyze and describe seismic catalogs and to perform short-term forecasting. The standard errors of parameter estimates in the ETAS model are significant and cannot be ignored. This paper uses simulations to explore the accuracy of conventional standard error estimates based on the Hessian matrix of the log-likelihood function of the ETAS model. We show that such error estimates are not accurate when the observed space-time window is small. One must only cautiously trust the Hessian-based standard error estimates for this model when using local datasets with time windows of several years in length. The standard errors for all parameter estimates introduced by magnitude errors in typical earthquake catalogs are found to be smaller than those introduced by choosing a finite time window. However, neither effect is insignificant.

Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing

AbstractIn this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in multiple cracked bodies. The Zienkiewicz–Zhu error estimator is employed in conjunction with the modified superconvergent patch recovery (SPR) technique to obtain more accurate estimation of error. A stability analysis is performed to determine active cracks from a set of competitive cracks. Various crack growth criteria together with the respective crack trajectory prediction are compared. Several numerical examples are illustrated to demonstrate the efficiency, robustness and accuracy of computational algorithm in the simulation of multiple crack growth. Copyright © 2010 John Wiley & Sons, Ltd.

Optimizing working parameters of the smooth particle mesh Ewald algorithm in terms of accuracy and efficiency

We construct an accurate error estimate for the root mean square force error of the smooth particle mesh Ewald (SPME) algorithm, which is often used for molecular dynamics simulations, where charge configurations under periodic boundary conditions require considerable amounts of CPU time. The error estimates are provided for the ik- as well as analytical force differentiation schemes, and their validity is tested for a random homogeneous sample system. Finally, we demonstrate that it is possible to straightforwardly and precisely determine the SPME parameters via the error estimates prior to the simulation for a predetermined accuracy. This can save precious computer and user time and allows an easy choice of a suitable parameter set for nearly optimal speed.

A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations

The implementation of quadratic velocity, linear pressure finite element approximation methods for the steady-state incompressible (Navier–)Stokes equations is addressed in this work. Three types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true discretisation error. Computational results suggest that the solution of local Poisson problems provides a cost-effective error estimation strategy, both from the perspective of accurate estimation of the global error and for the purpose of selecting elements for refinement within a contemporary self-adaptive refinement algorithm.

The PCSE Estimator is Good -- Just Not As Good As You Think

This paper investigates the properties of the Panel-Corrected Standard Error (PCSE) estimator. The PCSE estimator is commonly used when working with time-series, cross-sectional (TSCS) data. In an influential paper, Beck and Katz (1995) (henceforth BK) demonstrated that FGLS produces coefficient standard errors that are severely underestimated. They report Monte Carlo experiments in which the PCSE estimator produces accurate standard error estimates at no or little loss in efficiency compared to FGLS. Our study further investigates the properties of the PCSE estimator. We first reproduce the main experimental results of BK using their Monte Carlo framework. We then show that the PCSE estimator does not perform as well when tested in data environments that better resemble “practical research situations.” When (i) the explanatory variable(s) are characterized by substantial persistence, (ii) there is serial correlation in the errors, and (iii) the time span of the data series is relatively short, coverage rates for the PCSE estimator frequently fall between 80 and 90 percent. Further, we find many “practical research situations” where the PCSE estimator compares poorly with FGLS on efficiency grounds.

Estimating the Variability of Estimated Variance Components for Generalizability Theory

Generalizability theory is widely applied in psychological and educational measurement.The variability of estimated variance component,which is constrained by sampling,is the "Achilles heel" of generalizability theory. Therefore,estimating the variability of estimated variance components needs to be further explored. In previous literature,some problems remain to be settled:first,the previous studies failed to compare the variability of estimated variance components among different methods simultaneously:traditional,bootstrap,jackknife and Markov Chain Monte Carlo (MCMC); second,some studies only focused on such variability of estimated variance components as the standard error,while neglected other variability such as confidence interval; last but not least,MCMC method which can be used in generalizability theory hasn't gained sufficient exploration. There are different methods to estimate the variability of variance components:standard error and confidence interval,including traditional,bootstrap,jackknife and MCMC. Based on these four methods,the study adopts Monte Carlo data simulation technique to compare the variability of estimated variance components for normal distribution data. For traditional method,ANOVA is used to estimate the variance components and their standard errors. Satterthwaite and TBGJL are used to estimate the confidence intervals. For bootstrap method,twelve bootstrap strategies are adopted,but only three strategies are considered in jackknife method and only two strategies,i.e.,informative and non-informative priors,for MCMC method. Some criteria are set to compare the four methods. The bias is cared about when variance components and their standard errors are estimated. The smaller the absolute bias is,the more reliable the result is. The criterion of confidence intervals is "80% interval coverage". If the "80% interval coverage" is more closed to 0.80,the confidence interval is more reliable. The simulation is implemented in R statistical programming environment. To link R program with WinBUGS,R2WinBUGS and Coda package are adopted. And the simulation results are as follows. First,it is more accurate to use traditional,jackknife,adjusted bootstrap and MCMC method with informative priors to estimate variance components. But unadjusted bootstrap and MCMC method with non-informative priors are not adequate. Second,traditional and MCMC method with informative priors are accurate to estimate standard errors of three variance components,while jackknife method is not. Bootstrap method needs to adopt a "divide-and-conquer" strategy to obtain good estimated standard errors:the most accurate estimation of standard error for person is consistently provided by adjusted boot-p or boot-ir; adjusted boot-pi is the clear winner in estimating standard error for item; adjusted boot-ir,boot-pir or boot-pr give good estimate of standard error for person and item. Finally,using traditional and MCMC method to estimate confidence intervals is suitable because their respective interval coverages are close to 0.80. But jackknife method is not accurate in estimating confidence intervals. There is no great difference between Bootstrap-PC and Bootstrap-BCa method that are used to estimate confidence intervals of three variance components. Bootstrap method should apply the "divide-and-conquer" strategy to get desirable estimated confidence intervals as following:adjusted boot-p for person; adjusted boot-pi for item; adjusted boot-ir,boot-pr or boot-p for person and item. This study shows that jackknife method is not accurate to estimate the variability of estimated variance components. If the "divide-and-conquer" strategy is not used in bootstrap method,it is advisable to use traditional method or MCMC method with informative priors.

THE SLOAN LENS ACS SURVEY. IX. COLORS, LENSING, AND STELLAR MASSES OF EARLY-TYPE GALAXIES

We present the current photometric dataset for the Sloan Lens ACS (SLACS) Survey, including HST photometry from ACS, WFPC2, and NICMOS. These data have enabled the confirmation of an additional 15 grade `A' (certain) lens systems, bringing the number of SLACS grade `A' lenses to 85; including 13 grade `B' (likely) systems, SLACS has identified nearly 100 lenses and lens candidates. Approximately 80% of the grade `A' systems have elliptical morphologies while ~10% show spiral structure; the remaining lenses have lenticular morphologies. Spectroscopic redshifts for the lens and source are available for every system, making SLACS the largest homogeneous dataset of galaxy-scale lenses to date. We have developed a novel Bayesian stellar population analysis code to determine robust stellar masses with accurate error estimates. We apply this code to deep, high-resolution HST imaging and determine stellar masses with typical statistical errors of 0.1 dex; we find that these stellar masses are unbiased compared to estimates obtained using SDSS photometry, provided that informative priors are used. The stellar masses range from 10^10.5 to 10^11.8 M$_\odot$ and the typical stellar mass fraction within the Einstein radius is 0.4, assuming a Chabrier IMF. The ensemble properties of the SLACS lens galaxies, e.g. stellar masses and projected ellipticities, appear to be indistinguishable from other SDSS galaxies with similar stellar velocity dispersions. This further supports that SLACS lenses are representative of the overall population of massive early-type galaxies with M* >~ 10^11 M$_\odot$, and are therefore an ideal dataset to investigate the kpc-scale distribution of luminous and dark matter in galaxies out to z ~ 0.5.

Accurate and rapid error estimation on global gravitational field from current GRACE and future GRACE Follow-On missions

Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser (K-band) ranging system, the orbital position and velocity of a global positioning system (GPS) receiver and non-conservative force of an accelerometer, is established from the perspectives of the power spectrum principle in physics using the semi-analytical approach. Secondly, the accuracy of the global gravitational field is accurately and rapidly estimated based on the combined error model; the cumulative geoid height error is 1.985 × 10−1 m at degree 120 based on GRACE Level 1B measured observation errors of the year 2007 published by the US Jet Propulsion Laboratory (JPL), and the cumulative geoid height error is 5.825 × 10−2 m at degree 360 using GRACE Follow-On orbital altitude 250 km and inter-satellite range 50 km. The matching relationship of accuracy indexes from GRACE Follow-On key payloads is brought forward, and the dependability of the combined error model is validated. Finally, the feasibility of high-accuracy and high-resolution global gravitational field estimation from GRACE Follow-On is demonstrated based on different satellite orbital altitudes.

Modeling of cohesive crack growth using an adaptive mesh refinement via the modified-SPR technique

In this paper, an adaptive finite element procedure is presented in modeling of mixed-mode cohesive crack propagation via the modified superconvergent path recovery technique. The adaptive mesh refinement is performed based on the Zienkiewicz–Zhu error estimator. The weighted-SPR recovery technique is employed to improve the accuracy of error estimation. The Espinosa–Zavattieri bilinear cohesive zone model is applied to implement the traction-separation law. It is worth mentioning that no previous information is necessary for the path of crack growth and no region of the domain is necessary to be filled by the cohesive elements. The maximum principal stress criterion is employed for predicting the direction of extension of the cohesive crack in order to implement the cohesive elements. Several numerical examples are analyzed numerically to demonstrate the capability and efficiency of proposed computational algorithm.

Efficient Parameterization of the Observation Error Covariance Matrix for Square Root or Ensemble Kalman Filters: Application to Ocean Altimetry

Abstract In the Kalman filter standard algorithm, the computational complexity of the observational update is proportional to the cube of the number y of observations (leading behavior for large y). In realistic atmospheric or oceanic applications, involving an increasing quantity of available observations, this often leads to a prohibitive cost and to the necessity of simplifying the problem by aggregating or dropping observations. If the filter error covariance matrices are in square root form, as in square root or ensemble Kalman filters, the standard algorithm can be transformed to be linear in y, providing that the observation error covariance matrix is diagonal. This is a significant drawback of this transformed algorithm and often leads to an assumption of uncorrelated observation errors for the sake of numerical efficiency. In this paper, it is shown that the linearity of the transformed algorithm in y can be preserved for other forms of the observation error covariance matrix. In particular, quite general correlation structures (with analytic asymptotic expressions) can be simulated simply by augmenting the observation vector with differences of the original observations, such as their discrete gradients. Errors in ocean altimetric observations are spatially correlated, as for instance orbit or atmospheric errors along the satellite track. Adequately parameterizing these correlations can directly improve the quality of observational updates and the accuracy of the associated error estimates. In this paper, the example of the North Brazil Current circulation is used to demonstrate the importance of this effect, which is especially significant in that region of moderate ratio between signal amplitude and observation noise, and to show that the efficient parameterization that is proposed for the observation error correlations is appropriate to take it into account. Adding explicit gradient observations also receives a physical justification. This parameterization is thus proved to be useful to ocean data assimilation systems that are based on square root or ensemble Kalman filters, as soon as the number of observations becomes penalizing, and if a sophisticated parameterization of the observation error correlations is required.