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Measurement errors are often encountered in several continuous variables in a data set, and various methods have been proposed to handle these measurement errors when they are supposed to be independent. Recently, Kekeç and Van Keilegom (Electron J Stat 16(1):1831–1854, 2022) considered bivariate classical measurement error models with correlated measurement errors, and estimated their variance matrix when no validation data nor auxiliary variables are available. However, in practice, one often observes more than two variables with correlated measurement errors. In this paper, we introduce a flexible and practical method to estimate the variance matrix of multivariate classical additive Gaussian measurement errors, without additional information. We show that the error variance matrix is identifiable under certain circumstances and introduce an estimation method of the variance matrix and of the multivariate density of the variables of interest by means of Bernstein polynomials. Asymptotic properties and finite sample characteristics of the proposed methodology are also examined. Furthermore, we consider in a simulation study a multiple linear regression model with measurement errors in multiple covariates, and use the proposed estimator of the variance matrix to estimate the model parameters by means of the simulation extrapolation (SIMEX) algorithm. Finally, the method is illustrated on a dataset on fetal biometry measurements. [ABSTRACT FROM AUTHOR]

Systems of whole‐stand yield models facilitate projections of forest attributes, but their inputs may be difficult to measure accurately. This study conducted sensitivity analyses to examine the effect of systematic and stochastic measurement errors on outputs from a representative system of equations. Simulated error was added to explanatory variables stand age, site index, or both. Results showed that large systematic error in one variable tended to produce moderate to large percent changes in all models, particularly the height and volume equations (often >50% change). Systematic error in both variables amplified this effect, especially for young, less productive stands. Stochastic error dramatically increased estimate variability (some relative standard errors >50%), particularly in the height and volume models at young ages and low site indices. These results suggest that measurement error may considerably alter projections and increase uncertainty when using whole‐stand yield models, highlighting the need for careful crew training. Recommendations for Resource Managers: Measurement error in input variables has the potential to significantly affect estimates from systems of whole‐stand yield models.Effects can be over‐ or underestimation of volume yields and financial returns or other forest attributes of interest.Careful crew training is paramount to ensure forest measurements remain consistent with the quality of the data used to fit the models. [ABSTRACT FROM AUTHOR]

Scatter corrections are commonly applied to refine near‐infrared (NIR) spectra. The aim of this study is to assess the impact of measurement errors when using ordinary least squares (OLS) for multiplicative scatter correction (MSC). Any measurement errors attached to the set‐mean spectrum may attenuate the OLS slope and that in turn will affect the estimate of the intercept and the adjustment of the spectra when using MSC methods to mitigate scattering. A corrected least squares slope may be used instead to prevent this problem, although the impact of this approach on the final outcome will depend on the relative size of the measurement errors in the individual spectra and the set‐mean spectrum. The errors‐in‐variables or type II regression model (also known as Deming regression) and its special cases, major axis (MA) and reduced major axis (RMA), are discussed and illustrated. The extent of OLS slope bias or attenuation is demonstrated as is the resulting MSC spectral distortion. Further modification to the MSC transformation method is also suggested. The influence of scattering correction (by MSC, standard normal variate (SNV) and detrending) and of using the maximum likelihood estimate of the slope for MSC on the prediction of chemical composition of Lucerne herbage from NIR spectra was assessed. The predictive performance was slightly improved by the use of scattering corrections with fairly minor differences among methods. Nonetheless, it seems well worth considering the use of type II regression models for assessing MSC application aiming at improving the goodness of prediction from NIR spectra. [ABSTRACT FROM AUTHOR]

Nonparametric linear mixed effects models are preferred due to overcome the restrictions of linear models which need to satisfy distributional assumptions. In these models, smoothing approaches are needed to handle nonparametric part and chosen according to the type of data. When there is a measurement error in the nonparametric part, these smoothing techniques become more complicated. In this paper, we propose wavelet approach to smooth nonparametric function under known measurement error in nonparametric linear mixed effects model and then, we predict random effects pa rameter. Furthermore, as imulation study is done to demonstrate the theoretical findings by comparing with the case ignoring measurement error. The performances are much better for the proposed model than the no measurement error case. [ABSTRACT FROM AUTHOR]

Measurement errors and missing data are often arise in practice. Under this circumstance, we focus on using jackknife empirical likelihood (JEL) and adjust jackknife empirical likelihood (AJEL) methods to construct confidence intervals for the error variance in linear models. Based on residuals of the models, the biased-corrected inverse probability weighted estimator of the error variance is introduced. Furthermore, we propose the jackknife estimator, jackknife and adjust jackknife empirical log-likelihood ratios of the error variance and establish their asymptotic distributions. Simulation studies in terms of coverage probability and average length of confidence intervals are conducted to evaluate the proposed method. A real data set is used to illustrate the proposed JEL and AJEL methods. [ABSTRACT FROM AUTHOR]

Population size estimation is an important research field in biological sciences. In practice, covariates are often measured upon capture on individuals sampled from the population. However, some biological measurements, such as body weight, may vary over time within a subject's capture history. This can be treated as a population size estimation problem in the presence of covariate measurement error. We show that if the unobserved true covariate and measurement error are both normally distributed, then a naïve estimator without taking into account measurement error will under-estimate the population size. We then develop new methods to correct for the effect of measurement errors. In particular, we present a conditional score and a nonparametric corrected score approach that are both consistent for population size estimation. Importantly, the proposed approaches do not require the distribution assumption on the true covariates; furthermore, the latter does not require normality assumptions on the measurement errors. This is highly relevant in biological applications, as the distribution of covariates is often non-normal or unknown. We investigate finite sample performance of the new estimators via extensive simulated studies. The methods are applied to real data from a capture–recapture study. Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

In this paper, we consider least squares estimation and empirical likelihood inference for partial functional linear models when the covariates in the non-functional linear component are measured with additive error and the responses are missing at random. Asymptotic properties of the proposed estimators for the parametric and nonparametric components are established. A class of empirical log-likelihood ratio functions of the parametric component and response mean are developed, and the corresponding maximum empirical likelihood estimators are constructed. We also prove that the empirical log-likelihood ratio functions are asymptotic standard chi-squared distribution. The results can be used to construct confidence intervals for the parametric component and response mean. The asymptotic distributions of the corresponding maximum empirical likelihood estimators are also established. Meanwhile, a simulation study is conducted to demonstrate the finite sample performance of the proposed procedure. A real data analysis is also used to illustrate our methods. [ABSTRACT FROM AUTHOR]

This paper studies how to estimate and test the symmetry of a continuous variable under the additive distortion measurement errors setting. The unobservable variable is distorted in a additive fashion by an observed confounding variable. Firstly, a direct plug-in estimation procedure is proposed to calibrate the unobserved variable. Next, we propose four test statistics for testing whether the unobserved variable is symmetric or not. The asymptotic properties of the proposed estimators and test statistics are investigated. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

A logarithmic calibration estimation procedure is proposed for nonparametric regression models under the multiplicative distortion measurement errors setting. The unobservable response variable and covariates are both distorted in a multiplicative fashion by an observed confounding variable. By using the logarithmic calibration estimation procedure for unobserved variables, we consider to study the estimates of nonparametric mean function and its first derivative, the variance function, the Sharpe ratio function and correlation curve. We obtain asymptotic normality results for the proposed nonparametric estimators. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyse a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

Estimating the impact of a treatment on a given response is needed in many biomedical applications. However, methodology is lacking for the case when the response is a continuous temporal curve, treatment covariates suffer extensively from measurement error, and even the exact timing of the treatments is unknown. We introduce a novel method for this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information across individuals, and a sparse Gaussian process for the baseline trend. Importantly, our model accounts for errors not only in treatment covariates, but also in treatment timings, a problem arising in practice for example when data on treatments are based on user self-reporting. We validate our model with simulated and real patient data, and show that in a challenging application of estimating the impact of diet on continuous blood glucose measurements, accounting for measurement error significantly improves estimation and prediction accuracy. [ABSTRACT FROM AUTHOR]

Rounding error is an important source of measurement error that is common in index data. The problem can be traced to rounding that occurs to limit the number of digits after the decimal place to be reported in rebased index data. Rounding error introduces distortions that affect variance properties, alter the lag distributions of time series models, and cause a systematic bias in estimated coefficients. For instance, spuriously choppy inflation rates are obtained when constructed using the official CPI, rebased with 1982-84 = 100. Fortunately, the distortions can be generally avoided by using versions of data that have greater precision. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. First, we investigate estimations in varying-coefficient partially linear errors-in-variables models with covariates missing at random. However, the estimators are often biased due to the existence of measurement errors, the bias-corrected profile least-squares estimator and local liner estimators for unknown parametric and coefficient functions are obtained based on inverse probability weighted method. The asymptotic properties of the proposed estimators both for the parameter and nonparametric parts are established. Second, we study asymptotic distributions of an empirical log-likelihood ratio statistic and maximum empirical likelihood estimator for the unknown parameter. Based on this, more accurate confidence regions of the unknown parameter can be constructed. The methods are examined through simulation studies and illustrated by a real data analysis. [ABSTRACT FROM AUTHOR]

A correlation curve measures the strength of the association between two variables locally at different values of covariate. This paper studies how to estimate the correlation curve under the multiplicative distortion measurement errors setting. The unobservable variables are both distorted in a multiplicative fashion by an observed confounding variable. We obtain asymptotic normality results for the estimated correlation curve. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimator. The estimated correlation curve is applied to analyze a real dataset for an illustration. [ABSTRACT FROM AUTHOR]

This article studies the sensitivity of Granger causality to the addition of noise, the introduction of subsampling, and the application of causal invertible filters to weakly stationary processes. Using canonical spectral factors and Wold decompositions, we give general conditions under which additive noise or filtering distorts Granger‐causal properties by inducing (spurious) Granger causality, as well as conditions under which it does not. For the errors‐in‐variables case, we give a continuity result, which implies that: a 'small' noise‐to‐signal ratio entails 'small' distortions in Granger causality. On filtering, we give general necessary and sufficient conditions under which 'spurious' causal relations between (vector) time series are not induced by linear transformations of the variables involved. This also yields transformations (or filters) which can eliminate Granger causality from one vector to another one. In a number of cases, we clarify results in the existing literature, with a number of calculations streamlining some existing approaches. [ABSTRACT FROM AUTHOR]

• The aim of this study was to calibrate gillnet catches using Fish Biomass per Area obtained by active methods. • We found a strong positive linear relationship between fish biomasses sampled with gillnets and with active methods. • The effective sampling area of 1 m2 of gillnet was determined to be 8 m2 of surface area for European standard gillnets. Fish are an important component of aquatic ecosystems, thus representative and reliable assessments of their population variables are essential for a variety of ecological applications, management and conservation. Determining Fish Density per actual Spatial Unit (volume or area, FDSU) as a measure of absolute fish quantity is of particular interest. Gillnets are undoubtedly one of the most common and important methods for assessing fish populations in large lentic waters. However, direct calculating of FDSU from gillnet catches is impossible because of the passive nature of this method, and to date there is no reliable model for calculating FDSU from gillnet catches. This weakness largely limits the use of gillnet data for applications requiring FDSU estimates. The aim of this study was to calibrate gillnet catches using FDSU obtained by active methods (beach seine nets and hydroacoustics) to develop a tool for assessing FDSU from gillnet catches. To achieve this goal, we compared gillnet biomass to fish biomass estimated from the active methods, both of which cover similar spatiotemporal niches. This comparison was performed using a statistical approach based on the recognition of non-negligible random measurement error in both the explanatory (active methods) and response (gillnets) variables. We found a strong positive linear relationship between fish biomasses sampled with gillnets and with active methods. The slope of the fitted linear model was similar when comparing gillnets with the two active methods. The statistical method used allowed for the inclusion of error in the biomass estimates with gillnets and active methods, refining the credible intervals of the estimated relationship. The effect of gillnet effort on model accuracy was simulated to show how increased effort narrows the credible interval. Finally, comparison with previously published relationships revealed a large but explainable discrepancy between our model and previous models. Our study showed that conversion of gillnet biomass to biomass per actual spatial unit is possible. The effective sampling area of one square meter of gillnet was determined to be 8 m2 of waterbody surface area when European standard 12 mesh-sizes gillnets are used, and 5 m2 when four larger meshes are added to the European standard gillnets. Our model further stressed the impact of increased sampling effort on reducing estimation variability and shows that the model may be dependent on the fish community. [ABSTRACT FROM AUTHOR]

We study partial linear single-index models (PLSiMs) when the response and the covariates in the parametric part are measured with additive distortion measurement errors. These distortions are modeled by unknown functions of a commonly observable confounding variable. We use the semiparametric profile least-squares method to estimate the parameters in the PLSiMs based on the residuals obtained from the distorted variables and confounding variable. We also employ the smoothly clipped absolute deviation penalty (SCAD) to select the relevant variables in the PLSiMs. We show that the resulting SCAD estimators are consistent and possess the oracle property. For the non parametric link function, we construct the simultaneous confidence bands and obtain the asymptotic distribution of the maximum absolute deviation between the estimated link function and the true link function. A simulation study is conducted to evaluate the performance of the proposed methods and a real dataset is analyzed for illustration. [ABSTRACT FROM PUBLISHER]

This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a additive fashion by an observed confounding variable. Two estimators, a direct-plug-in estimator and a residual-based estimator, are proposed. Their asymptotical results are obtained, and the residual-based estimator is shown asymptotically efficient. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence interval. The empirical likelihood statistic is shown to be asymptotically chi-squared. Simulation studies are conducted to examine the performance of the proposed estimators. These methods are applied to analyse the Boston housing price data for an illustration. [ABSTRACT FROM PUBLISHER]

A linearerrors-in-variables(EIV) model that contains measurement errors in the input and output data is considered.Weakly dependent(α- and ϕ-mixing) errors, not necessarily stationary nor identically distributed, are taken into account within the EIV model. Parameters of the EIV model are estimated by thetotal least squaresapproach, which provideshighly non linearestimates. Because of this, many statistical procedures for constructing confidence intervals and testing hypotheses cannot be applied. One possible solution to this dilemma is ablock bootstrap. An appropriate moving block bootstrap procedure is provided and its correctness proved. The results are illustrated through a simulation study and applied on real data as well. [ABSTRACT FROM PUBLISHER]

Missing observations and covariate measurement error commonly arise in longitudinal data. However, existing methods for model selection in marginal regression analysis of longitudinal data fail to address the potential bias resulting from these issues. To tackle this problem, we propose a new model selection criterion, the Generalized Longitudinal Information Criterion, which is based on an approximately unbiased estimator for the expected quadratic error of a considered marginal model accounting for both data missingness and covariate measurement error. The simulation results reveal that the proposed method performs quite well in the presence of missing data and covariate measurement error. On the contrary, the naive procedures without taking care of such complexity in data may perform quite poorly. The proposed method is applied to data from the Taiwan Longitudinal Study on Aging to assess the relationship of depression with health and social status in the elderly, accommodating measurement error in the covariate as well as missing observations. [ABSTRACT FROM AUTHOR]

This review article considers some of the most common methods used in astronomy for regressing one quantity against another in order to estimate the model parameters or to predict an observationally expensive quantity using trends between object values. These methods have to tackle some of the awkward features prevalent in astronomical data, namely heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection and selection effects, data structure and non-uniform population (often called Malmquist bias), non-Gaussian data, outliers, and mixtures of regressions. We outline how least square fits, weighted least squares methods, Maximum Likelihood, survival analysis, and Bayesian methods have been applied in the astrophysics literature when one or more of these features is present. In particular we concentrate on errors-in-variables regression and we advocate Bayesian techniques. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 6: 15-33, 2013 [ABSTRACT FROM AUTHOR]

We consider kernel density estimation when the observations are contaminated by measurement errors. It is well-known that the success of kernel estimators depends heavily on the choice of a smoothing parameter called the bandwidth. A number of data-driven bandwidth selectors exist, but they are all global. Such techniques are appropriate when the density is relatively simple, but local bandwidth selectors can be more attractive in more complex settings. We suggest several data-driven local bandwidth selectors and illustrate via simulations the significant improvement they can bring over a global bandwidth. [ABSTRACT FROM AUTHOR]

Measurement errors in spawner abundance create problems for fish stock assessment scientists. To deal with measurement error, we develop a Bayesian state-space model for stock-recruitment data that contain measurement error in spawner abundance, process error in recruitment, and time series bias. Through extensive simulations across numerous scenarios, we compare the statistical performance of the Bayesian state-space model with that of standard regression for a traditional stock-recruitment model that only considers process error. Performance varies depending on the information content in data, as determined by stock productivity, types of harvest situations, and amount of measurement error. Overall, in terms of estimating optimal spawner abundance S MSY , the Ricker density-dependence parameter β, and optimal harvest rate h MSY , the Bayesian state-space model works best for informative data from low and variable harvest rate situations for high-productivity salmon stocks. The traditional stock-recruitment model (TSR) may be used for estimating α and h MSY for low-productivity stocks from variable and high harvest rate situations. However, TSR can severely overestimate S MSY when spawner abundance is measured with large error in low and variable harvest rate situations. We also found that there is substantial merit in using h MSY (or benchmarks derived from it) instead of S MSY as a management target. [Copyright &y& Elsevier]

In linear models for hedge fund returns, errors-in-variables may significantly alter the measurement of factor loadings and the estimation of abnormal performance. The higher moment estimator (HME) introduced by Dagenais and Dagenais (1997) effectively deals with these issues. Results on individual funds show that the HME specification does not uncover systematic performance biases, but can modify estimated alphas in most cases and identifies relative persistence for directional funds in bearish market conditions. Overall, the risk premia calculated with HME remain relatively stable when compared to ordinary least squares specifications. [ABSTRACT FROM AUTHOR]

Abstract: The problem introduced by grouping income data when measuring socioeconomic inequalities in health (and health care) has been highlighted in a recent study in this journal. We re-examine this issue and show there is a tendency to underestimate the concentration index at an increasing rate when lowering the number of income categories. This tendency arises due to a form of measurement error and we propose two correction methods. Firstly, the use of instrumental variables (IV) can reduce the error within income categories. Secondly, through a simple formula for correction that is based only on the number of groups. We find that the simple correction formula reduces the impact of grouping and always outperforms the IV approach. Use of this correction can substantially improve comparisons of the concentration index both across countries and across time. [Copyright &y& Elsevier]

In a lot of situations, variables are measured with errors. While this problem has been previously studied in the context of kernel regression, no work has been done in quantile regression. To estimate this function, we use deconvolution kernel estimators. We obtain asymptotic results (MSE and normality) for two estimators of conditional quantiles and analyse their finite sample performances via a large simulation study. [ABSTRACT FROM AUTHOR]

Predicting the value of a variable Y corresponding to a future value of an explanatory variable X, based on a sample of previously observed independent data pairs (X1, Y1),..., (X1, Y1) distributed like (X, Y), is very important in statistics. In the error-free case, where Xis observed accurately, this problem is strongly related to that of standard regression estimation, since prediction of Y can be achieved via estimation of the regression curve E(YIX). When the observed X,s and the future observation of X are measured with error, prediction is of a quite different nature. Here, if T denotes the future (contaminated) available version of X, prediction of Y can be achieved via estimation of E(YIT). In practice, estimating E(YIT) can be quite challenging, as data may be collected under different conditions, making the measurement errors on X and X nonidentically distributed. We take up this problem in the nonparametric setting and introduce estimators which allow a highly adaptive approach to smoothing. Reflecting the complexity of the problem, optimal rates of convergence of estimators can vary from the semiparametric n-1/2 rate to much slower rates that are characteristic of nonparametric problems. Nevertheless, we are able to develop highly adaptive, data-driven methods that achieve very good performance in practice. This article has the supplementary materials online. [ABSTRACT FROM AUTHOR]

The linear model with classical measurement error is an alternative to the standard regression model, in which it is assumed that the independent variables are subject to error. This assumption can cause statistical inferences and parameter estimators to differ dramatically from those obtained by the standard regression model. However, in some cases, inferences remain unchanged even though the independent variables are assumed to be subject to error. This article investigates the invariance property of score tests for assessing heteroscedasticity, first-order autoregressive disturbance, and the need for a Box-Cox power transformation. Under specific constraints, we show that the score tests for measurement error models are identical to the corresponding well-established tests derived from standard regression models. Hence practitioners can assess assumptions of constant variance and independent errors, as well as the need for a Box-Cox transformation, irrespective of whether or not the variables are measured with error. We also discuss some possible generalizations. [ABSTRACT FROM AUTHOR]

In many situations, variables are measured with errors. Though this problem has been studied previously in the context of kernel regression, the results have been applied to the case where only the covariates are contaminated. This article addresses the problem where both (covariates and response variables) are contaminated. We estimate the conditional mode function. To estimate this function, we use deconvoluting kernel estimators. The asymptotic behavior of these estimators depends on the smoothness of the noise distribution. Asymptotic normality is established for strongly mixing stochastic processes, when the error distribution is smooth. [ABSTRACT FROM AUTHOR]

We introduce a new method, moment reconstruction, of correcting for measurement error in covariates in regression models. The central idea is similar to regression calibration in that the values of the covariates that are measured with error are replaced by “adjusted” values. In regression calibration the adjusted value is the expectation of the true value conditional on the measured value. In moment reconstruction the adjusted value is the variance-preserving empirical Bayes estimate of the true value conditional on the outcome variable. The adjusted values thereby have the same first two moments and the same covariance with the outcome variable as the unobserved “true” covariate values. We show that moment reconstruction is equivalent to regression calibration in the case of linear regression, but leads to different results for logistic regression. For case–control studies with logistic regression and covariates that are normally distributed within cases and controls, we show that the resulting estimates of the regression coefficients are consistent. In simulations we demonstrate that for logistic regression, moment reconstruction carries less bias than regression calibration, and for case–control studies is superior in mean-square error to the standard regression calibration approach. Finally, we give an example of the use of moment reconstruction in linear discriminant analysis and a nonstandard problem where we wish to adjust a classification tree for measurement error in the explanatory variables. [ABSTRACT FROM AUTHOR]

SUMMARY A modified estimating equation approach is proposed to correct for measurement error in regression problems. We allow changing measurement error variances and covariances across units, allow the regressors to be fixed, allow estimation of the measurement error variances/covariances and account for uncertainty arising from this estimation, and explicitly model measurement error in the response. Multiple linear, quadratic, Poisson, and logistic regression are considered in detail and it is seen that some previously developed estimators arise as special cases from the proposed approach. A small simulation study is presented for logistic regression. [ABSTRACT FROM AUTHOR]