Uncorrelated Measurement Errors Research Articles

Estimation of population mean using ranked set sampling in the presence of measurement errors

Ranked set sampling is widely acknowledged for its superior efficiency compared with simple random sampling. Only a small amount of work has been conducted using ranked set sampling when measurement errors are present. This study introduces innovative estimators utilizing ranked set sampling to assess the population mean when faced with both correlated and uncorrelated measurement errors. The expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation, revealing their superior performance compared to the other examined estimators. The efficacy of the suggested estimators in handling measurement errors was demonstrated through numerical illustration and simulation study investigations. The recommended estimators are further compared to the existing ones using the percentage relative efficiency and mean squared error, and the impact of measurement errors on the results is highlighted through the percentage computation of measurement errors. The innovative estimators suggested were formulated by judiciously incorporating ratio, exponential, and log estimators. Numerical examples involving expenditure and income, as well as simulated data generated from a normal population using R software, affirm the superior performance of the proposed estimators over existing ones such as the usual mean estimator and those proposed by Vishwakarma and Singh (2022), as evidenced by the higher percent relative efficiency and lower mean squared error. The evaluation of the percentage contribution of measurement error values confirms the impact of measurement errors on the properties of the estimators.

Modelling Factors Affecting Internally Generated Funds of the Tamale Metropolitan Assembly of Ghana Using Multivariate Analysis Techniques

Abstract The study was carried out to model factors that affect the Internally Generated Funds of the Tamale Metropolitan Assembly using Factor and Confirmatory Factor analysis. The study involved 403 categories of respondents using probability and non-probability sampling techniques. The results from the Factor analysis confirmed a four-factor structure model to accurately represent the observed data without substantial loss of information. The Factor analysis revealed that the four factors affecting Internally Generated Funds in the metropolis are a proper database on revenue mobilisation, effectiveness and efficiency of revenue collectors, revenue monitoring and utilisation, and specific tools deployed for revenue mobilisation. Further examination of the Factor analysis using Confirmatory Factor analysis revealed that some modifications to the four-factor structure model in terms of correlating the measurement errors provide a good fit to the observed data as compared to a four-factor structure model with uncorrelated measurement errors. Findings from the Sattora-Bentler parameter estimates conclude that all paths of the selected model were significant, thus confirming a relationship between all latent variables and each measured variable of Internally Generated Funds. The findings from the study suggest further research on the use of the Structural Equation Model in an analogous area to be instituted to measure and analyse relationships between measured and latent variables.

Underwater Navigation of AUVs Using Uncorrelated Measurement Error Model of USBL

<i>This article presents a modeling method for the uncorrelated measurement error of the ultra-short baseline (USBL) acoustic positioning system for aiding navigation of underwater vehicles. The Mahalanobis distance (MD) and principal component analysis are applied to decorrelate the errors of USBL measurements, which are correlated in the x- and y-directions and vary according to the relative direction and distance between a reference station and the underwater vehicles. The proposed method can decouple the radial-direction error and angular direction error from each USBL measurement, where the former and latter are independent and dependent, respectively, of the distance between the reference station and the vehicle. With the decorrelation of the USBL errors along the trajectory of the vehicles in every time step, the proposed method can reduce the threshold of the outlier decision level. To demonstrate the effectiveness of the proposed method, simulation studies were performed with motion data obtained from a field experiment involving an autonomous underwater vehicle and USBL signals generated numerically by matching the specifications of a specific USBL with the data of a global positioning system. The simulations indicated that the navigation system is more robust in rejecting outliers of the USBL measurements than conventional ones. In addition, it was shown that the erroneous estimation of the navigation system after a long USBL blackout can converge to the true states using the MD of the USBL measurements. The navigation systems using the uncorrelated error model of the USBL, therefore, can effectively eliminate USBL outliers without loss of uncontaminated signals.</i>

Computing the effect of measurement errors on ranked set sampling estimators of the population mean

SummaryThe effect of measurement errors shows the seriousness of the estimators or the estimation procedures and cannot be avoided in sensitive cases because “a miss is as good as a mile.” In this article, we have proposed the very first ranked set estimators like unbiased, ratio, product, difference, ratio exponential, and product exponential estimators under both correlated and uncorrelated measurement errors. The expressions for bias and mean square error of the proposed estimators are obtained up to the first order of approximation. The proposed ranked set estimators have been compared through relative efficiencies over unbiased estimators and the effect of measurement errors has been given through percentage computation of measurement errors. The theoretical conditions are obtained under which the proposed estimator has performed better. The performance of the proposed ranked set estimators under measurement errors are shown by efficiency comparisons, Monte‐Carlo simulation study, and real data study.

The Effects of Uncorrelated Measurement Noise on SWOT Estimates of Sea Surface Height, Velocity, and Vorticity

Abstract The Ka-band Radar Interferometer (KaRIn) on the Surface Water and Ocean Topography (SWOT) satellite will revolutionize satellite altimetry by measuring sea surface height (SSH) with unprecedented accuracy and resolution across two 50-km swaths separated by a 20-km gap. The original plan to provide an SSH product with a footprint diameter of 1 km has changed to providing two SSH data products with footprint diameters of 0.5 and 2 km. The swath-averaged standard deviations and wavenumber spectra of the uncorrelated measurement errors for these footprints are derived from the SWOT science requirements that are expressed in terms of the wavenumber spectrum of SSH after smoothing with a filter cutoff wavelength of 15 km. The availability of two-dimensional fields of SSH within the measurement swaths will provide the first spaceborne estimates of instantaneous surface velocity and vorticity through the geostrophic equations. The swath-averaged standard deviations of the noise in estimates of velocity and vorticity derived by propagation of the uncorrelated SSH measurement noise through the finite difference approximations of the derivatives are shown to be too large for the SWOT data products to be used directly in most applications, even for the coarsest footprint diameter of 2 km. It is shown from wavenumber spectra and maps constructed from simulated SWOT data that additional smoothing will be required for most applications of SWOT estimates of velocity and vorticity. Equations are presented for the swath-averaged standard deviations and wavenumber spectra of residual noise in SSH and geostrophically computed velocity and vorticity after isotropic two-dimensional smoothing for any user-defined smoother and filter cutoff wavelength of the smoothing.

Methods of mutual high-precision navigation based the use of relative modes of anglemeasuring receivers of global navigation satellite systems signals

The article presents the results of experimental studies of mutual high-precision navigation methods for unmanned and specialized transport systems. The proposed methods are based on the application of the relative operating modes of two or more angle-measuring receivers of global navigation satellite systems signals. To conduct research, a software and hardware complex has been developed, consisting of two angle-measuring receivers of global navigation satellite systems signals, a turntable and a computer model of the navigation system of unmanned and specialized transport systems. It provides the positioning error of the antenna system in angular coordinates less than 1 arc minute, which allows it to be used as a reference when measuring the angular displacements of the receiver of global navigation satellite systems signals antenna system. The results of measurements of planar and angular coordinates both in autonomous and relative phase modes of operation of goniometric receivers global navigation satellite systems signals are presented and analyzed. It has been established that the root-mean-square error of measuring relative coordinates was 0,019 meter. A further increase in the relative position measurement accuracy is possible by taking measures to reduce the multipath reception error, which is the most significant uncorrelated position measurement error by two sets of receivers of global navigation satellite systems signals. Thus, the methods of mutual high-precision navigation using angle-measuring receivers of global navigation satellite systems signals have high accuracy without the use of external information about differential corrections. This will allow the operation of unmanned or special transport systems in hard-toreach and northern regions, in conditions of lack of communication and other adverse factors.

The Influence of Measurement Errors on Generalized Estimator of Population Mean

This paper proposed a generalized estimator of population mean in the presence of correlated and uncorrelated measurement errors under simple random strategy. Some known estimators belong to this class of proposed estimator. Under the large sample approximation, the properties of the proposed estimator namely bias and mean squared error were obtained. Theoretical comparison was carried out on the members of the proposed class of estimators when measurement errors are correlated and when they are uncorrelated and the necessary conditions under which the proposed estimator at its optimum value is expected to be more efficient than the existing estimators of finite population mean were obtained. It was observed that correlated and uncorrelated measurement errors inflate the bias and mean squared error of the proposed estimator. The paper concluded that the proposed estimator is more efficient than usual unbiased estimator and some members of the class of proposed estimator.

Novel Algorithm for Mutual Alignment of Railway Track Geometry Measurements

Track geometry measurements are regularly collected to monitor the condition of a railway network. To detect deterioration patterns and enable predictive maintenance, sequential measurement runs must be mutually aligned which has been proven a serious challenge. This paper presents a novel algorithm for mutual alignment of track geometry signal data. It resolves several previously intractable alignment problems: highly segmented data with variable sample rate, spatially correlated and uncorrelated measurement errors, convergence to true locations, and consistency over time. The algorithm adjusts spatial measurement errors by splitting signals in continuous segments. Re-sampled, error-corrected signals are mutually aligned using cross correlation, and this process is repeated until the mutual alignment meets a pre-defined precision threshold. Missing measurement values are handled by imputing an interpolated offset from nearby segments, ensuring that the signals remain continuous. By using weighted average offsets over all aligned signals, the law of large numbers guarantees convergence and consistency. The practical feasibility of the algorithm is demonstrated on empirical track geometry measurement data from the British railway network, owned and operated by Network Rail.

Calibration under measurement errors

The calibration technique is the process of adjusting weights for the better enhancement of the estimate of the population parameters using auxiliary information. In this manuscript, we have proposed ratio and regression type calibration estimators for the population mean under both correlated and uncorrelated measurement errors. The variances of the proposed calibrated estimators to the first order approximation are obtained and compared their efficiencies. A Monte Carlo simulation study has been carried out to show the effect of measurement errors on the proposed calibrated estimators.

The Bias in Two-Pass Regression Tests of Asset-Pricing Models in Presence of Idiosyncratic Errors with Cross-Sectional Dependence

In two-pass regression-tests of asset-pricing models, cross-sectional correlations in the errors of the first-pass time-series regression lead to correlated measurement errors in the betas used as explanatory variables in the second-pass cross-sectional regression. The slope estimator of the second-pass regression is an estimate for the factor risk-premium and its significance is decisive for the validity of the pricing model. While it is well known that the slope estimator is downward biased in presence of uncorrelated measurement errors, we show in this paper that the correlations seen in empirical return data substantially suppress this bias. For the case of a single-factor model, we calculate the bias of the OLS slope estimator in the presence of correlated measurement errors with a first-order Taylor-approximation in the size of the errors. We show that the bias increases with the size of the errors, but decreases the more the errors are correlated. We illustrate and validate our result using a simulation approach based on empirical data commonly used in asset-pricing tests.

Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity

Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity

Accounting for Berkson and Classical Measurement Error in Radon Exposure Using a Bayesian Structural Approach in the Analysis of Lung Cancer Mortality in the French Cohort of Uranium Miners.

Many occupational cohort studies on underground miners have demonstrated that radon exposure is associated with an increased risk of lung cancer mortality. However, despite the deleterious consequences of exposure measurement error on statistical inference, these analyses traditionally do not account for exposure uncertainty. This might be due to the challenging nature of measurement error resulting from imperfect surrogate measures of radon exposure. Indeed, we are typically faced with exposure uncertainty in a time-varying exposure variable where both the type and the magnitude of error may depend on period of exposure. To address the challenge of accounting for multiplicative and heteroscedastic measurement error that may be of Berkson or classical nature, depending on the year of exposure, we opted for a Bayesian structural approach, which is arguably the most flexible method to account for uncertainty in exposure assessment. We assessed the association between occupational radon exposure and lung cancer mortality in the French cohort of uranium miners and found the impact of uncorrelated multiplicative measurement error to be of marginal importance. However, our findings indicate that the retrospective nature of exposure assessment that occurred in the earliest years of mining of this cohort as well as many other cohorts of underground miners might lead to an attenuation of the exposure-risk relationship. More research is needed to address further uncertainties in the calculation of lung dose, since this step will likely introduce important sources of shared uncertainty.

Validation of the Urdu version of the Measure of Criminal Social Identity within a sample of Pakistani incarcerated delinquents

Purpose – The purpose of this paper is to examine the dimensionality, composite reliability, and incremental validity of the Measure of Criminal Social Identity (MCSI) in a sample of Pakistani incarcerated delinquents (n=315) following translation of the measure into Urdu. Design/methodology/approach – Four alternative factor models, with uncorrelated measurement error terms, were specified and tested using confirmatory factor analysis and bifactor modelling techniques. Findings – Results indicated that a three-factor model provided a better fit to the data than the alternative models tested. The reliability of the scale was established using composite reliability. Furthermore, structural equation modelling revealed that the three MCSI factors were differentially related with external variables, indicating that the MCSI measures substantially different domains. Research limitations/implications – Implications for theory and future research are discussed. Originality/value – The results add valuable evidence as to the cross-cultural applicability of the MCSI.

Correlated measurement error hampers association network inference.

Modern chromatography-based metabolomics measurements generate large amounts of data in the form of abundances of metabolites. An increasingly popular way of representing and analyzing such data is by means of association networks. Ideally, such a network can be interpreted in terms of the underlying biology. A property of chromatography-based metabolomics data is that the measurement error structure is complex: apart from the usual (random) instrumental error there is also correlated measurement error. This is intrinsic to the way the samples are prepared and the analyses are performed and cannot be avoided. The impact of correlated measurement errors on (partial) correlation networks can be large and is not always predictable. The interplay between relative amounts of uncorrelated measurement error, correlated measurement error and biological variation defines this impact. Using chromatography-based time-resolved lipidomics data obtained from a human intervention study we show how partial correlation based association networks are influenced by correlated measurement error. We show how the effect of correlated measurement error on partial correlations is different for direct and indirect associations. For direct associations the correlated measurement error usually has no negative effect on the results, while for indirect associations, depending on the relative size of the correlated measurement error, results can become unreliable. The aim of this paper is to generate awareness of the existence of correlated measurement errors and their influence on association networks. Time series lipidomics data is used for this purpose, as it makes it possible to visually distinguish the correlated measurement error from a biological response. Underestimating the phenomenon of correlated measurement error will result in the suggestion of biologically meaningful results that in reality rest solely on complicated error structures. Using proper experimental designs that allow for the quantification of the size of correlated and uncorrelated errors, can help to identify suspicious connections in association networks constructed from (partial) correlations.

The Impact of Measurement Error on Principal Component Analysis

ABSTRACTWe investigate the effect of measurement error on principal component analysis in the high‐dimensional setting. The effects of random, additive errors are characterized by the expectation and variance of the changes in the eigenvalues and eigenvectors. The results show that the impact of uncorrelated measurement error on the principal component scores is mainly in terms of increased variability and not bias. In practice, the error‐induced increase in variability is small compared with the original variability for the components corresponding to the largest eigenvalues. This suggests that the impact will be negligible when these component scores are used in classification and regression or for visualizing data. However, the measurement error will contribute to a large variability in component loadings, relative to the loading values, such that interpretation based on the loadings can be difficult. The results are illustrated by simulating additive Gaussian measurement error in microarray expression data from cancer tumours and control tissues.

The factor structure and composite reliability of the Rosenberg Self-Esteem Scale among ex-prisoners

The aim of this study was to examine the factor structure and composite reliability of the Rosenberg Self-Esteem Scale (RSES) using a sample of 669 ex-prisoners identified in the National Survey of American Life. Six distinct factor models, with uncorrelated measurement error terms, were specified and tested using confirmatory factor analysis (CFA). Results indicated that the two-factor model consisting of positive and negative latent variables provided a better fit to the data than the alternative models. Moreover, only positive self-esteem was a significant predictor of recidivism. Composite reliability indicated that the two factors were measured with very good reliability. The results consequently provide additional support for a two-dimensional model of the RSES within offender populations.

Statistical Aspects of the Use of Biomarkers in Nutritional Epidemiology Research

Few strong and consistent associations have arisen from observational studies of dietary consumption in relation to chronic disease risk. Measurement error in self-reported dietary assessment may be obscuring many such associations. Attempts to correct for measurement error have mostly used a second self-report assessment in a subset of a study cohort to calibrate the self-report assessment used throughout the cohort, under the dubious assumption of uncorrelated measurement errors between the two assessments. The use, instead, of objective biomarkers of nutrient consumption to produce calibrated consumption estimates provides a promising approach to enhance study reliability. As summarized here, we have recently applied this nutrient biomarker approach to examine energy, protein, and percent of energy from protein, in relation to disease incidence in Women's Health Initiative cohorts, and find strong associations that are not evident without biomarker calibration. A major bottleneck for the broader use of a biomarker-calibration approach is the rather few nutrients for which a suitable biomarker has been developed. Some methodologic approaches to the development of additional pertinent biomarkers, including the possible use of a respiratory quotient from indirect calorimetry for macronutrient biomarker development, and the potential of human feeding studies for the evaluation of a range of urine- and blood-based potential biomarkers, will briefly be described.

Markov properties in presence of measurement noise

Recently, several powerful tools for the reconstruction of stochastic differential equations from measured data sets have been proposed [e.g., Siegert, Phys. Lett. A 243, 275 (1998); Hurn, J. Time Series Anal. 24, 45 (2003)]. Efficient application of the methods, however, generally requires Markov properties to be fulfilled. This constraint typically seems to be violated on small scales, which frequently is attributed to physical effects. On the other hand, measurement noise such as uncorrelated measurement and discretization errors has large impacts on the statistics of measurements on small scales. We demonstrate that the presence of measurement noise, likewise, spoils Markov properties of an underlying Markov process. This fact is promising for the further development of techniques for the reconstruction of stochastic processes from measured data, since limitations at small scales might stem from artificial noise sources rather than from intrinsic properties of the dynamics of the underlying process. Measurement noise, however, can be controlled much better than the intrinsic dynamics of the underlying process.

A Constrained Least Squares Approach to Mobile Positioning: Algorithms and Optimality

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramer-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.

Measurement Error in Linear Autoregressive Models

Time series data are often subject to measurement error, usually the result of needing to estimate the variable of interest. Although it is often reasonable to assume that the measurement error is additive (i.e., the estimator is conditionally unbiased for the missing true value), the measurement error variances often vary as a result of changes in the population/process over time and/or changes in sampling effort. In this article we address estimation of the parameters in linear autoregressive models in the presence of additive and uncorrelated measurement errors, allowing heteroscedasticity in the measurement error variances. We establish the asymptotic properties of naive estimators that ignore measurement error and propose an estimator based on correcting the Yule–Walker estimating equations. We also examine a pseudo-likelihood method based on normality assumptions and computed using the Kalman filter. We review other techniques that have been proposed, including two that require no information about the measurement error variances, and compare the various estimators both theoretically and via simulations. The estimator based on corrected estimating equations is easy to obtain and readily accommodates (and is robust to) unequal measurement error variances. Asymptotic calculations and finite-sample simulations show that it is often relatively efficient.