Measurement Error Problems Research Articles

Suppression of cross-interference in the absorption spectra of gas mixtures

In the quantitative analysis of mixed gases by tunable diode laser absorption spectroscopy, the overlapping of absorption spectra and mutual interference of multi-component gases can lead to problems of large measurement errors and low analysis accuracy. In this paper, an improved firefly algorithm is proposed and applied to the support vector machine regression model to solve this problem. The specific method includes introducing an adaptive step size to balance the local and global searches and using the gradient descent method to accelerate the parameter optimization process so as to improve the model’s generalization ability and prediction accuracy. The experimental results show that the maximum errors of the improved algorithm in the prediction of CH4 and CO gas concentrations are no more than 0.0443 % and 2 ppm, with coefficients of determination, R2, of 0.9994 and 0.99815. The promising results obtained by the system provide theoretical support for the realization of high-precision detection of multicomponent gases with a single source of light, and also demonstrate the high efficiency and feasibility of the method in practical detection.

A multilevel lightweight fish respiratory frequency measurement method – Segmentation instead of detection

Respiratory frequency is an important physiological parameter for fish health. Traditional respiration detection methods have inherent frequency measurement error problems, and segmentation provides an innovative technique for respiration measurement. By shifting the focus from detection to segmentation, this approach provides robust and reliable support for measuring fish respiratory frequency accurately. However, the existing segmentation network models face challenges related to their large scale, high computational demands, and limited deployability at the edge. To overcome these challenges, this paper introduces an easily portable, high-precision segmentation method based on lightweight network and network slimming technique, named PM-YOLOv5s-seg (Prune MobileNetv3-YOLOv5s Segmentation). PM-YOLOv5s-seg utilizes the MobileNetv3 network as its segmentation backbone, enabling the extraction of essential fish mouth features. Simultaneously, it employs depth separable convolution to reduce network parameters and calculation amounts. Furthermore, the model undergoes additional sparsification via channel pruning, significantly improving its efficiency. Finally, respiratory frequency modeling is performed on the obtained fish mouth segmentation results, utilizing innovative techniques such as Ellipse fitting, Kalman filtering, and polynomial fitting methods. Comparison with the state-of-the-art methods demonstrates the superiority of the multilevel lightweight segmentation model PM-YOLOv5s-seg in terms of detection accuracy, computational efficiency, and model size. This model achieves an optimal balance between the speed and accuracy in fish respiratory frequency measurement, which holds significant implications for fish welfare as well as disease detection.

The Gaussian distribution: Derivation method and its applications in selected examples

Gaussian distribution is the most important and common form of distribution in statistical theory, and its density function has more complicated forms. When Gauss dealt with the problem of measurement error, he derived the form of normal distribution from another angle, and proposed the least squares theory based on the normal distribution of error. This helps solve the problem of the probability density distribution of the error, enabling people to make a better statistical measure of the effect of the size of the error. In short, Gaussian distribution is not only a powerful mathematical tool, but also a connection between theory and practical applications. It is also a bridge between theory and practical application. In practice, the Gaussian distribution has a wide range of applications, in the natural sciences, engineering and social sciences and other fields, the Gaussian distribution is used to describe the continuity of random variables, such as measurement error, temperature change, population intelligence level. In this paper, the author briefly deduces the Gaussian distribution derivation process, from the overall and the measurement error of the simple random samples to cut in, to admit that x is already the estimates that should be taken. Hopefully, it will be helpful to scholars who are interested in this area.

Measurement error in longitudinal earnings data: evidence from Germany

We present evidence on the extent of measurement error in German longitudinal earnings data. Qualitatively, we confirm the main result of the international literature: longitudinal earnings data are relatively reliable in a cross section but much less so in first differences. Quantitatively, in the cross section our findings are very similar to those of Bound and Krueger (J Labor Econ 9:1–24, 1991) and Pischke (J Bus Econ Stat 13:305–314, 1995) for the United States while we find even stronger evidence that first-differencing exacerbates measurement error problems. We also show that measurement error in our survey data is not “classical” as it is negatively correlated with administrative earnings and positively autocorrelated over an extended period of time. Additionally, we estimate a model of measurement error stemming from underreporting of transitory earnings shocks in combination with a white-noise component and make a number of methodological contributions. Our results are robust to the use of two different linked survey-administrative data sets and various other sensitivity checks.

Intangible Capital in Factor Models

The transition from a traditional manufacturing-based economy to a knowledge- and service-based economy over recent decades resulted in a considerable rise in intangible capital, most of which is not reported on companies’ balance sheets. As a result, balance sheet-based valuation ratios, investment measures, and other firm characteristics that do not incorporate off-balance sheet (OBS) intangible capital suffer from significant measurement error problems. We incorporate a new measure of OBS intangible capital into firm characteristics, such as book to market, investment, and profitability, to address these measurement errors. These OBS intangible adjustments improve the performance of the Fama–French three- and five-factor models and the q-factor model, especially during recent decades. We further find that the value factor is no longer redundant in these empirical factor models. This paper was accepted by Lukas Schmid, finance. Funding: The authors are grateful for financial support from the 2019 EDHEC Scientific Beta “Advanced ESG & Factor Investing” Research Chair. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01261 .

Research on Full-Field Dynamic Deflection Measurement of Beams Based on Dense Feature Matching and Mismatch Removal Method

To solve the problems of measurement errors led by mismatches of dense feature matching in machine vision structural deflection measurement, this paper proposes a dense feature extraction, matching, and dual-step mismatch-removal-based full-field structural dynamic deflection measurement method. First, the of dense feature detection and matching theory is introduced to extract the SIFT feature points on a structural surface in an image sequence and matched by FLANN to trace the structure movement, and the mechanisms and causes of mismatches are analyzed. Then, a dual-step mismatch removal method combining RANSAC and Structural Displacement Continuity Restriction (SDCR) is introduced to achieve full-field dynamic beam deflection measurement. The proposed method is validated through indoor cantilever beam experiments, and results show that the method can effectively eliminate a large number of SIFT feature mismatches (accounting for approximately 55% of the total matched feature points). The full-field dynamic displacement field of the beam can be measured with the correctly matched dense feature points by converting dense feature point displacements into continuous and uniform spatiotemporal deflections of the structure. A comparison with the GOM Correlate Professional DIC measurement system was conducted, and the maximum measurement error of the cantilever beam dynamic displacement of the proposed method is between 0.024 and 0.053 mm, the root mean squared error of displacement is approximately 0.01 mm, and the correlation coefficient between two deflection–time curves reaches 0.9964. The proposed algorithm is proven to be effective in full-field displacement measurement and has great potential in future structural health monitoring of bridges.

Estimation of Quadratic Food Engel Curve in the presence of Measurement Error and Endogeneity of Total Expenditure in Pakistan

This study is conducted to compare the four different estimation techniques, Ordinary least square, Instrumental Variable, Lewbel (1996) approach and control function approach estimating the quadratic food Engel curve in the presence of the problem of measurement error and the problem of endogeneity of total expenditure. The authors have used the HIES data 2010-11 as it has been observed that the HIES data 2010-11 fits a quadratic shape of food Engel curve in Pakistani context. Moreover, the expenditure elasticity of food demand was observed between zero and one which indicates the fact that food is a necessary good for Pakistani households. The results also shows that endogeneity of total expenditure is more serious issue than the measurement error.

A method for measuring and adaptively correcting lens center thickness based on the chromatic confocal principle

Optical systems are widely used in aerospace, life sciences, civil livelihood and other fields. The lens is one of the most common components in optical systems, and its centre thickness is an important parameter in material characterization and manufacturing process, which directly affects the performance and function of optical components. In this paper, based on the chromatic confocal principle and laser interference technology, we propose a method applied to the measurement and adaptive correction of lens centre thickness, aiming to solve the problem of lens centre thickness measurement error. We successfully built an adaptive error correction system and proposed a translation correction algorithm and a tilt correction algorithm. This method not only can accurately measure the lens thickness but also can adaptively compensate for the measurement error caused by the lack of accuracy of mechanical elements or motion mechanisms through the spatial attitude correction of the element to be measured. The experimental results show that this method has obvious advantages in the translation error correction and tilt error correction of the lens. After the translation correction, the measurement accuracy of the lens is improved by about 75.21%; after the tilt correction, the measurement accuracy of the lens is improved by about 71.48%.

Robust estimation of mean-variance relation.

Accurate assessment of the mean-variance relation can benefit subsequent analysis in biomedical research. However, in most biomedical data, both the true mean and the true variance are unavailable. Instead, raw data are typically used to allow forming sample mean and sample variance in practice. In addition, different experimental conditions sometimes cause a slightly different mean-variance relation from the majority of the data in the same data set. To address these issues, we propose a semiparametric estimator, where we treat the uncertainty in the sample mean as a measurement error problem, the uncertainty in the sample variance as model error, and use a mixture model to account for different mean-variance relations. Asymptotic normality of the proposed method is established and its finite sample properties are demonstrated by simulation studies. The data application shows that the proposed method produces sensible results compared with methods either ignoring the uncertainty in the sample means or ignoring the potential different mean-variance relations.

Commentary: On measurement error, PSA doubling time, and prostate cancer

Exposure measurement error is a pervasive problem for epidemiology research projects designed to provide valid and precise statistical evidence supporting postulated exposure-disease relationships of interest. The purpose of this commentary is to highlight an important real-life example of this exposure measurement error problem and to provide a simple and useful diagnostic tool for physicians and their patients that corrects for the exposure measurement error. More specifically, prostate-specific antigen doubling time (PSADT) is a widely used measure for guiding future treatment options for patients with biochemically recurrent prostate cancer. Numerous papers have been published claiming that a low calculated PSADT value (denoted PSADT̂) is predictive of metastasis and premature death from prostate cancer. Unfortunately, none of these papers have adjusted for the measurement error in PSADT̂, an estimator that is typically computed using the popular Memorial Sloan Kettering website very often visited by both physicians and their patients. For this website, the estimator PSADT̂ of the true (but unknown) PSADT for a patient (denoted PSADT∗) is computed as the natural log of 2 (i.e., 0.6931) divided by the estimated slope of the straight-line regression of the natural log of PSA (in ng/mL) on time. We utilize PSADT̂ to derive an expression for the probability that the unknown PSADT∗ for a patient is below a specified value C (>0) of concern to both the physician and the patient. This probability is easy to interpret and takes into account the fact that PSADT̂ is a statistical estimator with variability. This variability introduces measurement error, namely, the difference between a computed value PSADT̂ and the true, but unknown, value PSADT∗. We have developed an Excel calculator that, once the [time, ln(PSA)] values are entered, outputs both the value of PSADT̂ and the desired probability. In addition, we discuss problematic statistical issues attendant with PSADT∗ estimation typically based on at most three or four PSA values. We strongly recommend the use of this probability when physicians are discussing PSADT̂ values and associated treatment options with their patients. And, we stress that future epidemiology research projects involving PSA doubling time should take into account the measurement error problem highlighted in this Commentary.

Fast multi-feature tracking method based on tightly coupled sensors

In contrast to conventional methods of optimizing feature-matching results at the data-processing level, we utilize the tightly coupled mode to fuse the information collected by the camera and inertial sensor at the data-gathering level, which contributed to better accuracy and robustness in the feature-matching process. Specifically, the proposed visual-inertial feature tracking method that combines inertial measurement unit (IMU) calibration, feature matching, and prediction algorithms. The approach includes a vision-aided multi-level IMU systemic calibration method and an inertial-aided image feature prediction algorithm, which effectively processes and utilizes information from multiple sensors. Our method addresses not only the influence of image distortion and blur resulting from illumination changes and fast camera motion but also the problem of measurement errors that can arise from the long-term operation of the inertial sensors. Extensive experiments have been conducted to demonstrate that the efficiency of it is superior to the state-of-the-art methods: With the accuracy rate remains the same level, the speed of feature matching is improved by 41.8%. Additionally, when it is applied to simultaneous localization and mapping systems, its localization performances are better than that of the VINS-mono method by 8.1%.

Calibration Method of a Wideband AC Resistance Voltage Divider Based on an Equivalent Model.

Aiming at the problem of large measurement error and phase shift in resistance voltage dividers under high-frequency conditions in the field of power measurement, such as power harmonics, an error correction method is proposed for an alternating current (AC) resistance voltage divider based on the equivalence principle. Firstly, the frequency error model of the AC resistance voltage divider precision is established, and the angle difference of the continuous spectrum ratio difference from 50 Hz to 100 kHz is corrected by determining the shielding structure and the resistance parameters and fine-tuning the shielding potential correction method to reduce the capacities error of the AC resistance voltage divider design precision. At the same time, the performance parameters such as the direction and magnitude of the shielding potential compensation capacitive error are investigated. Finally, the precision voltage divider (the maximum voltage applied is 480 V) calibration experiments verify that the important characteristic judgment factor of the voltage divider is independent of the frequency and the equivalent capacitance value, which effectively solves the phase correction problem of harmonic power measurement.

Estimation with mixed data frequencies: A bias-correction approach

We propose a solution to the measurement error problem that plagues the estimation of the relation between the expected return of the stock market and its conditional variance due to the latency of these conditional moments. We use intra-period returns to construct a nonparametric proxy for the latent conditional variance in the first step which is subsequently used as an input in the second step to estimate the parameters characterizing the risk–return tradeoff via a GMM approach. We propose a bias-correction to the standard GMM estimator derived under a double asymptotic framework, wherein the number of intra-period returns, N, as well as the number of low frequency time periods, T, are simultaneously large. Simulation exercises show that the bias-correction is particularly relevant for small values of N which is the case in empirical scenarios involving long time periods. The methodology lends itself to additional applications, such as the empirical evaluation of factor models, wherein the factor betas may be estimated using intra-period returns and the unexplained returns or alphas subsequently recovered at lower frequencies.

A spline-assisted semiparametric approach to nonparametric measurement error models

A spline-assisted approach is proposed to handle the measurement error problem in treating the pollution and asthma data. It is well known that the minimax rate of convergence in nonparametric regression function estimation of a random variable measured with error is much slower than the rate in the error free case. A different problem is considered. It is shown that if one is willing to impose a relatively mild assumption in requiring that the error-prone variable has a compact support, then standard nonparametric results are obtainable for measurement error models. New and constructive methods to take full advantage of the compact support assumption via spline-assisted semiparametric methods are proposed. It is proven that the new estimator achieves the usual nonparametric rate as if there were no measurement error. Furthermore it is shown that similar spline approach can be used to assess the probability density function on a compact set, using observations with error, and the resulting estimator differs from the true density function only by a constant scale. In addition, it retains the nonparametric density convergence properties of the error free case. The performance of the new methods is demonstrated through simulations and the methods are implemented to analyze the relation between asthma and pollution.

Right-censored partially linear regression model with error in variables: application with carotid endarterectomy dataset.

This paper considers a partially linear regression model relating a right-censored response variable to predictors and an extra covariate with measured error. The main problem here is that censorship and measurement error problems need to be solved to estimate the model correctly. In this sense, we propose three modified semiparametric estimators obtained from local polynomial regression, kernel smoothing, and B-spline smoothing methods based on kernel deconvolution approach and synthetic data transformation. Here, kernel deconvolution technique is used to solve the measurement error problem in the model and synthetic data transformation is considered to add the effect of censorship to the estimation procedure, which is a very common method in the literature. The performances of the introduced estimators are compared in the detailed Monte-Carlo simulation study. In addition, Carotid endarterectomy data is used as real-world data example and results are presented. According to the results, it is seen that the deconvoluted local polynomial method gives more qualified estimates than other two methods.

Development of Automated Test Equipment to Improve the Measurement Uncertainty of Seismic Acceleration Sensors: Focusing on Tilting-Type Equipment

This study developed an automated seismic acceleration sensor test equipment to improve the high measurement uncertainty of existing test equipment with the tilting method. The equipment was developed by setting the legal standards for seismic acceleration sensor test equipment and the problems of existing test equipment as performance indicators. The problems with the existing test equipment, which was manually operated, included measurement error owing to handling vibration, occurrence of angle error according to the observation field, and measurement method without considering hysteresis. The developed equipment satisfied the legal standards, and the problem of measurement error owing to handling vibration and angle error according to the observation field of view was improved by attaching a servo motor and precision level to the measurement equipment. Hysteresis control has been improved by adding the delay time control function of dedicated software (S/W). The developed automated seismic acceleration sensor test equipment can be used for the testing of seismic acceleration sensors, and the operating software reduced measurement uncertainty in the testing of seismic acceleration sensors.

A TDOA/AOA Hybrid Positioning Based on Improved Sparrow Search Algorithm for Mobile Position Estimation

To address the difficulty in calculating the nonlinear equation of time difference of arrival (TDOA) positioning, as well as the problem of measurement error in the hybrid time difference of arrival/angle of arrival (TDOA/AOA) positioning algorithm, an improved sparrow search algorithm is proposed to optimize positioning, and the optimization mechanism is retained on the basis of improving the performance of the original algorithm. The maximum likelihood estimation method is used to calculate the objective function, and then, the estimated function of the mobile station is used as the fitness function to generate the initial population of sparrows. Then, using particle swarm optimization, optimize the sparrow search algorithm and obtain the population’s optimal solution in order to obtain the optimal position. The simulation results show that, when compared to the existing algorithm, increasing the number of base stations increases the average accuracy of the sparrow search algorithm (SSA) positioning method by 18.54% and 4.5%, respectively, and, when compared to the proposed particle swarm optimization (PSO) positioning method, by 13.79% and 11.6% as the radius increases. The SSA hybrid positioning algorithm performs better in terms of positioning accuracy, convergence speed, and robustness.

Does corruption affect firm growth? New evidence from Mozambique

This paper estimates the effect of corruption on firm growth; specifically, in the context of Mozambique. Using instrumental variable estimation to address potential problems of endogeneity and measurement error, the paper finds that corruption has a robust negative effect on sales and productivity growth. The effect is not constant but declines as firm performance drops and corruption increases. This means corruption is most damaging to high-performance firms, meaning firms with higher sales and productivity growth rates, and to firms with lower bribe rates. For low-performance firms and firms with higher bribe rates, the effect gradually approaches zero. The paper contributes to the literatures in two ways. First, it offers a more nuanced understanding of the relationship between corruption and firm growth by showing that the effect of corruption is conditional on firm-specific factors. Second, the paper extends the empirical research on corruption and firm growth to Southern Africa, which has previously been excluded from the literature.

Detecting and correcting for heteroscedasticity in the presence of measurement error

The problem of measurement error in predictors has received a vast amount of attention for both linear and non-linear models. The major focus has generally been on inference for regression coefficients, while residual analysis, variance estimation and heteroscedasticity assessment have received limited attention. In this paper we propose and evaluate new methods, based on reconstructed predictors, to address these problems in the context of linear regression. Methods using moment reconstructed predictors are found to perform well, including a new model-based bootstrapping technique for testing heteroscedasticity. Motivated by an example where the predictor is methylation rate and the measurement error model is based on the binomial distribution, particular attention is given to being able to handle the situation where both the measurement error variances and the variance of the error in the equation may be changing as a quadratic function of the unobserved predictor.

External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent

The present paper deals with the external identification of a reciprocal, special passive, 2n-port network under measurement uncertainties. In the present context, the multiport model is represented by an admittance matrix and the condition that the network is ‘reciprocal special passive’ refers to the assumption that the real part of the admittance matrix is symmetric and positive-definite. The key point is to reformulate the identification problem as a matrix optimization program over the matrix manifold S+(2n)×S(2n). The optimization problem requires a least-squares criterion function designed to cope with over-determinacy due to the incoherent data pairs whose cardinality exceeds the problem’s number of degrees of freedom. The present paper also proposes a numerical solution to such an optimization problem based on the Riemannian-gradient steepest descent method. The numerical results show that the proposed method is effective as long as reasonable measurement error levels and problem sizes are being dealt with.