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Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice., (© 2019 The International Biometric Society.)

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., (© The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

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]

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]

We consider the linear regression model with stochastic regressors and stochastic errors both in regressors and the dependent variable ("structural EIV model"), where the regressors and errors are assumed to satisfy some interesting and general conditions, different from traditional assumptions on EIV models (such as Deming regression). The most interesting fact is that we need neither independence of errors, nor identical distributions, nor zero means. The first main result is that the TLS estimator, where the traditional Frobenius norm is replaced by the Chebyshev norm, yields a consistent estimator of regression parameters under the assumptions summarized below. The second main result is that we design an algorithm for computation of the estimator, reducing the computation to a family of generalized linear-fractional programming problems (which are easily computable by interior point methods). The conditions under which our estimator works are (said roughly): it is known which regressors are affected by random errors and which are observed exactly; that the regressors satisfy a certain asymptotic regularity condition; all error distributions, both in regressors and in the endogenous variable, are bounded in absolute value by a common bound (but the bound is unknown and is estimated); there is a high probability that we observe a family of data points where the errors are close to the bound. We also generalize the method to the case that the bounds of errors in the dependent variable and regressors are not the same, but their ratios are known or estimable. The assumptions, under which our estimator works, cover many settings where the traditional TLS is inconsistent. [ABSTRACT FROM AUTHOR]

Semi-functional linear regression models are important in practice. In this paper, their estimation is discussed when function-valued and real-valued random variables are all measured with additive error. By means of functional principal component analysis and kernel smoothing techniques, the estimators of the slope function and the non parametric component are obtained. To account for errors in variables, deconvolution is involved in the construction of a new class of kernel estimators. The convergence rates of the estimators of the unknown slope function and non parametric component are established under suitable norm and conditions. Simulation studies are conducted to illustrate the finite sample performance of our method. [ABSTRACT FROM AUTHOR]

Growth value model (GVM) considers stock intrinsic value as the synergy of book value and return on equity (ROE), which contains two parameters, value factor and growth factor. This study addresses the problem of independent variables having measurement errors by utilizing errors-in-variables regression to estimate accurate model parameters. Research findings show the following: (1) The regression curve derived by traditional regression analysis exhibits severe bias. Errors-in-variables regression is capable of correcting the bias. (2) Large-scale firms exhibit lower value factor and higher growth factor, which indicates that large-scale firms possess better profit persistence. [ABSTRACT FROM AUTHOR]

This paper studies the strong consistency of some estimators for an errors-in-variables regression model. We first provide an extension of Meister's theorem. Then, the same problem is dealt with under the Fourier-oscillating noises. Finally, we prove two strong consistency theorems for wavelet estimators corresponding to non-oscillating and Fourier-oscillating noises. [ABSTRACT FROM AUTHOR]

The experimental design plays an important role in every experimental study. However, if errors in the settings of the studied factors cannot be avoided, i.e. Berkson errors occur, the estimates of the model parameters may be biased and the variability in the study increased. Correction methods for the effect of Berkson errors are compared. The emphasis is on the study of correlated Berkson errors which follow non-Gaussian distribution as this appears to have been a neglected, yet important, area. It is shown that the regression calibration approach bias correction methods are useful when the Berkson errors are independent. However, when these errors are dependent, the newly proposed method B-SIMEX clearly outperforms the other methods. [ABSTRACT FROM AUTHOR]

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]

Spatial climate variables are routinely used in species distribution models (SDMs) without accounting for the fact that they have been predicted with uncertainty, which can lead to biased estimates, erroneous inference and poor performances when predicting to new settings - for example under climate change scenarios., We show how information on uncertainty associated with spatial climate variables can be obtained from climate data models. We then explain different types of uncertainty (i.e. classical and Berkson error) and use two statistical methods that incorporate uncertainty in climate variables into SDMs by means of (i) hierarchical modelling and (ii) simulation-extrapolation., We used simulation to study the consequences of failure to account for measurement error. When uncertainty in explanatory variables was not accounted for, we found that coefficient estimates were biased and the SDM had a loss of statistical power. Further, this bias led to biased predictions when projecting change in distribution under climate change scenarios. The proposed errors-in-variables methods were less sensitive to these issues., We also fit the proposed models to real data (presence/absence data on the Carolina wren, Thryothorus ludovicianus), as a function of temperature variables., The proposed framework allows for many possible extensions and improvements to SDMs. If information on the uncertainty of spatial climate variables is available to researchers, we recommend the following: (i) first identify the type of uncertainty; (ii) consider whether any spatial autocorrelation or independence assumptions are required; and (iii) attempt to incorporate the uncertainty into the SDM through established statistical methods and their extensions. [ABSTRACT FROM AUTHOR]

Instrumental variable (IV) regression provides a number of statistical challenges due to the shape of the likelihood. We review the main Bayesian literature on instrumental variables and highlight these pathologies. We discuss Jeffreys priors, the connection to the errors-in-the-variables problems and more general error distributions. We propose, as an alternative to the inverted Wishart prior, a new Cholesky-based prior for the covariance matrix of the errors in IV regressions. We argue that this prior is more flexible and more robust thanthe inverted Wishart prior since it is not based on only one tightness parameter and therefore can be more informative about certain components of the covariance matrix and less informative about others. We show how prior-posterior inference can be formulated in a Gibbs sampler and compare its performance in the weak instruments case for synthetic as well as two illustrations based on well-known real data. [ABSTRACT FROM PUBLISHER]

Abstract: The magnetic properties of well-drained, near-neutral modern soils exhibit strong relationships with mean annual precipitation (MAP, conventional 30-year averages). The pedogenic magnetic susceptibility is low for low map values (≈300mm/yr), increases with increasing map (up to ≈1500mm/yr), and then flattens or declines for higher map values. These relationships have been amply documented, characterised quantitatively, and used for Quaternary palaeorainfall reconstructions. However, neither the fitting of climofunctions nor the evaluation of the associated uncertainty had yet been done recognizing the measurement errors that invariably affect the values of magnetic susceptibility and of map. Using published datasets – from the Great Plains of the United States, from the Chinese Loess Plateau and the Russian steppe, from arid and tropical areas of Mali, and from Mediterranean and Saharan regions of Morocco – we illustrate the development and calibration of statistical models that enable the use of magnetic properties of palaeosols as proxies for palaeorainfall. The methods we use (errors-in-variables regression) take into account the measurement errors that inevitably affect both the measurements of magnetic susceptibility, and of rainfall. We also characterise the uncertainty of the palaeoclimatic reconstructions that these models produce, and show that the uncertainty with which we can estimate the long-term (over hundreds of years) average values of map that truly characterise the prevailing climate, is sufficiently small to enable reliable palaeoclimate reconstructions. As an example, we provide an assessment of the uncertainty of the Holocene palaeorainfall reconstruction for Duowa, Qinghai Province, in the Chinese Loess Plateau, which corroborates the changes in the regimen of monsoons detected in previous studies. [Copyright &y& Elsevier]

As a compromise between parametric regression and nonparametric regression, partially linear models are frequently used in statistical modelling. This article considers statistical inference for this semiparametric model when the linear covariate is measured with additive error and some additional linear restrictions on the parametric component are assumed to hold. We propose a restricted corrected profile least-squares estimator for the parametric component, and study the asymptotic normality of the estimator. To test hypothesis on the parametric component, we construct a Wald test statistic and obtain its limiting distribution. Some simulation studies are conducted to illustrate our approaches. [ABSTRACT FROM AUTHOR]

The paper presents an approach to internal reliability analysis of observation systems known as Errors-in-Variables (EIV) models with parameters estimated by the method of least squares. Such problems are routinely treated by total least squares adjustment, or orthogonal regression. To create a suitable environment for derivations in the analysis, a general nonlinear form of such EIV models is assumed, based on a traditional adjustment method of condition equations with unknowns, also known as the Gauss-Helmert model. However, in order to apply the method of reliability analysis based on the approach to response assessment in systems with correlated observations, presented in the earlier work of this author, it was necessary to confine the considerations to a quasi-linear form of the Gauss-Helmert model, representing quasi-linear EIV models. This made it possible to obtain a linear disturbance/response relationship needed in that approach. Several specific cases of quasi-linear EIV models are discussed. The derived formulas are consistent with those already functioning for standard least squares adjustment problems. The analysis shows that, as could be expected, the average level of response-based reliability for such EIV models under investigation is lower than that for the corresponding standard linear models. For EIV models with homoscedastic and uncorrelated observations, the relationship between the average reliability indices for the independent and the dependent variables is formulated for multiple regression and coordinate transformations. Numerical examples for these two applications are provided to illustrate this analysis. [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]

Abstract: A great deal of interest has been paid to autoregressive parameter estimation in the noise-free case or when the observation data are disturbed by random noise. Tracking time-varying autoregressive (TVAR) parameters has been also discussed, but few papers deal with this issue when there is an additive zero-mean white Gaussian measurement noise. In this paper, one considers deterministic regression methods (or evolutive methods) where the TVAR parameters are assumed to be weighted combinations of basis functions. However, the additive white measurement noise leads to a weight-estimation bias when standard least squares methods are used. Therefore, we propose two alternative blind off-line methods that allow both the variance of the additive noise and the weights to be estimated. The first one is based on the errors-in-variable issue whereas the second consists in viewing the estimation issue as a generalized eigenvalue problem. A comparative study with other existing methods confirms the effectiveness of the proposed methods. [Copyright &y& Elsevier]

This article shows that the first autocorrelation of basketball shot results is a highly biased and inconsistent estimator of the first autocorrelation of the ex ante probabilities with which the shots are made. Shot result autocorrelation is close to zero even when shot probability autocorrelation is close to one. The bias is caused by what is equivalent to a severe measurement error problem. The results imply that the widespread belief among players and fans in the hot hand is not necessarily a cognitive fallacy. [ABSTRACT FROM AUTHOR]

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is predicated on minimizing the total sum of triangular areas formed between data points and the best fit line. Either of these methods is appropriately applied when both x and y are measured, a typical case in the natural sciences. In comparison to classical linear regression, equation derivation for the slope of the major axis and reduced major axis lines is a nontrivial process. For this reason, derivations are presented herein drawing from previous literature with as few steps as possible to enable an easily accessible understanding. Application to eruption data for Old Faithful geyser, Yellowstone National Park, Wyoming and Montana, USA enables a teaching opportunity for choice of model. [ABSTRACT FROM AUTHOR]

This paper proposes a wavelet (spectral) approach to estimate the parameters of a linear regression model where the regressand and the regressors are persistent processes and contain a measurement error. We propose a wavelet filtering approach which does not require instruments and yields unbiased estimates for the intercept and the slope parameters. Our Monte Carlo results also show that the wavelet approach is particularly effective when measurement errors for the regressand and the regressor are serially correlated. With this paper, we hope to bring a fresh perspective and stimulate further theoretical research in this area. [ABSTRACT FROM PUBLISHER]

We study a nonlinear regression problem of fitting a circle (or a circular arc) to scattered data. We prove that under any standard assumptions on the statistical distribution of errors that are commonly adopted in the literature, the orthogonal regression estimators of the circle center and radius have infinite (absolute) moments. We also discuss methodological implications of this fact. [ABSTRACT FROM AUTHOR]

Abstract: When researchers introduce a new test they have to demonstrate that it is valid, using unbiased designs and suitable statistical procedures. In this article we use Monte Carlo analyses to highlight how incorrect statistical procedures (i.e., stepwise regression, extreme scores analyses) or ignoring regression assumptions (e.g., heteroscedasticity) contribute to wrong validity estimates. Beyond these demonstrations, and as an example, we re-examined the results reported by concerning the validity of the Ability Emotional Intelligence Measure (AEIM). Warwick et al. used the wrong statistical procedures to conclude that the AEIM was incrementally valid beyond intelligence and personality traits in predicting various outcomes. In our re-analysis, we found that the reliability-corrected multiple correlation of their measures with personality and intelligence was up to .69. Using robust statistical procedures and appropriate controls, we also found that the AEIM did not predict incremental variance in GPA, stress, loneliness, or well-being, demonstrating the importance for testing validity instead of looking for it. [ABSTRACT FROM AUTHOR]

In this article, we propose a new empirical version of the Fama and French (F&F) model based on a new version of the Hausman (1978) specification test. This empirical model incorporates correction factors for risk exposure. These factors take into account the problem of errors-in-variables. Our model also features another innovation. It uses higher moments of the four factors of the augmented F&F model as instruments to tackle the problem of errors-in-variables. This new method reflects the nonlinear character of risk. We highlight the link between our new version of the Hausman artificial regression and the standard two-stage least-squares method. Our results suggest that it is preferable to account for errors-in-variables and more generally specification errors when estimating the F&F model because it might cause serious biases of important parameters like alpha and beta. [ABSTRACT FROM AUTHOR]

Abstract: We consider the nonparametric estimation of the regression functions for dependent data. Suppose that the covariates are observed with additive errors in the data and we employ nonparametric deconvolution kernel techniques to estimate the regression functions in this paper. We investigate how the strength of time dependence affects the asymptotic properties of the local constant and linear estimators. We treat both short-range dependent and long-range dependent linear processes in a unified way and demonstrate that the long-range dependence (LRD) of the covariates affects the asymptotic properties of the nonparametric estimators as well as the LRD of regression errors does. [Copyright &y& Elsevier]

Abstract: To increase the application domain (re-use) of LiDAR-based models the random replication effects in the predictor(s) must be considered. We quantify these effects in a linear predictor (X) of four forest inventory attributes (Lorey''s height HT, basal area BA, volume VOL, and stem density TPH) with LiDAR data acquired over 40 spruce-dominated large plots in southeastern Norway. A grid-based random thinning of the raw multi-echo LiDAR data, to five target densities between 0.25m−2 and 2.0m−2, generated 100 replications with each density. A DTM was estimated for each replicate and target pulse density. The four linear predictors were constructed from two indicators of canopy density and a posited average effect of a power-transform of echoes classified as canopy returns. Replication variance varied significantly among plots but the reliability ratio of X was high (≥0.92) for HT, BA and VOL but lower for TPH, especially at low pulse densities. Reliability ratios increased with pulse density. Replication variance attenuated the linear regression coefficients by about 10% and inflated the residual variance by 3–6%. A proposed calibration was effective in reducing the impact of replication effects. A proposed bootstrap procedure can be used in practice to obtain good approximations of the replication variance. With echo-densities of approximately 1m−2 or higher the replication effects do not warrant the effort of a calibration. [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]

This paper proposes a new estimator of regression coefficient in a linear model when both variables are observed with errors. Unlike previous estimators, the new estimator fully utilizes instrumental errors ratio (k) available to the experimental researcher. When compared to other estimators, our estimator is easy to use and provides an estimate with less bias. It is also a generalization of existing methods when k takes different values. [ABSTRACT FROM AUTHOR]

This article considers the problem of estimating linear model parameters from noisy measurements. The starting point is the classical approach by Koopmans for linear regression analysis. It is known that concerning the direct application of those early results for process identification, neither the original Koopmans algorithm nor its updated forms called Koopmans-Levin algorithms exhibit maximum-likelihood (ML) parameter estimation. In this article, a new, numerically advanced method is developed to ensure ML property for the parameter estimation, assuming noisy inputs and outputs, respectively. [ABSTRACT FROM AUTHOR]

Regression methods for the analysis of paired measurements produced by two fallible assay methods are described and their advantages and pitfalls discussed. The difficulties for the analysis, as in any errors-in-variables problem lies in the lack of identifiability of the model and the need to introduce questionable and often naïve assumptions in order to gain identifiability. Although not a panacea, the use of instrumental variables and associated instrumental variable (IV) regression methods in this area of application has great potential to improve the situation. Large samples are frequently needed and two-phase sampling methods are introduced to improve the efficiency of the IV estimators. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a recently developed regression model with noised variables in which the means of the response and some covariable components are nonparametric functions of an auxiliary variable. Previous results have shown that the de-noised estimators of the parameters of interest are asymptotically normal when undersmoothing is applied. But undersmoothing causes difficulties in bandwidth selection. To avoid this problem, we propose an empirical log-likelihood ratio for the regression coefficients and derive a nonparametric version of Wilk''s theorem. The confidence region based on the empirical likelihood has three advantages compared with those based on asymptotic normality: (1) It does not have the predetermined symmetry, which enables it to better reflect the true shape of the underlying distribution; (2) it does not involve any asymptotic covariance matrix estimation and hence is robust against the heteroscedasticity; and (3) it avoids undersmoothing the regressor functions so that optimal bandwidth can be used. A small simulation is conducted to compare the finite sample performances of these two methods. An example of application on a set of advertising data is also illustrated. [Copyright &y& Elsevier]

Oceanographers study past ocean circulations and their effect on global climate through carbon isotope records obtained from microfossils deposited on the ocean floor. An initial goal is to estimate the carbon isotope levels for the Pacific, Southern and North Atlantic Oceans over the last 23 million years and to provide confidence bands. We consider a nonparametric regression model and demonstrate how several recent developments in methodology make local linear kernel regression an attractive approach for tackling the problem. The results are used to estimate a quantity called the proportion of Northern Component Water and its effect on global climate. Several interesting and important geophysical and oceanographic conclusions are suggested by the study. [ABSTRACT FROM AUTHOR]

Abstract: We consider alternative models of a regression containing a proxy for an unobserved regressor. For each model at most two pieces of prior information are necessary to determine the sign of any regressor coefficient: the sign of the partial correlation between the proxy and the unobserved regressor, and a lower bound on the partial or simple correlation between the proxy and the unobserved regressor. We apply our technique to investment and leverage regressions that contain a proxy for the incentive to invest. In both cases proxy quality must be high for the coefficient of interest to be non-zero. [Copyright &y& Elsevier]

We compare the asymptotic relative efficiency of several regression calibration methods of correcting for measurement error in studies with internal validation data, when a single covariate is measured with error. The estimators we consider are appropriate in main study/hybrid validation study designs, where the latter study includes internal validation and may include external validation data. Although all of the methods we consider produce consistent estimates, the method proposed by Spiegelman et al. (Statistics in Medicine, 20 (2001) 139) has an asymptotically smaller variance than the other methods. The methods for measurement error correction are illustrated using a study of the effect of in utero lead exposure on infant birth weight. [Copyright &y& Elsevier]

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]

When estimating the treatment effect in a randomized controlled trial, it is common to have a continuous outcome which is also observed at baseline. These observations are often prone to measurement error, for example due to within-patient variability. Controversy exists in the literature about whether baseline measurement error should be adjusted for in this context. Computer simulations were used to compare the biases in the estimated treatment effect, with and without adjusting for measurement error, and for different levels of observed baseline imbalance. The impacts of sample size (30 per group and 300 per group) and reliability coefficient (0.6, 0.8 and 1) were also assessed. The results show that in randomized controlled trials, the ordinary least squares (OLS) estimator without adjusting for measurement error is unbiased. On the contrary, adjusting for measurement error leads to bias, especially when sample sizes are small and/or measurement error is large. The treatment effect adjusting for measurement error is on average overestimated when the baseline mean of the control group is larger than that of the treated group. It is underestimated when the control group has a smaller baseline mean. [Copyright &y& Elsevier]

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]

This paper advocates likelihood analysis for regression models with measurement errors in explanatory variables, for data problems in which the relevant distributions can be adequately modelled. Although computationally difficult, maximum likelihood estimates are more efficient than those based on first and second moment assumptions, and likelihood ratio inferences can be substantially better than those based on asymptotic normality of estimates. The EM algorithm is presented as a straightforward approach for likelihood analysis of normal linear regression with normal explanatory variables, and normal replicate measurements. [ABSTRACT FROM AUTHOR]

The estimator holding the central place in the theory of the multivariate "errors-in-the-variables" (EV) model results from performing orthogonal regression on variables rescaled according to the covariance matrix of the errors. Our simulations on the univariate model essentially relegate this estimator to use only in large samples on data with no trace of outlier contamination. A modification requiring a robust preliminary slope is proposed that essentially sets out the generalization to EV of the robust w-estimator in regression. It is demonstrated that the modification is robust to outlier contamination even in small samples, given a sufficiently good preliminary estimator. Candidates for a preliminary slope estimator based on the data are discussed and the performance of one under simulation is examined. [ABSTRACT FROM AUTHOR]

We consider several grouping tests for regression misspecification, with reference to housing-demand function estimation. We compare three existing test procedures, demonstrate modifications necessary in most applications, and propose a fourth test to distinguish between two categories of potential specification error. The test procedures are evaluated in artificial simulations of alternative errors. Finally, we apply the tests to FHA home purchase data. We reject the hypothesis that household and grouped regressions differ only by sampling error or random mismeasurement of household income or price. Our results have implications for choices among test procedures and interpretations of previous housing-demand analysis. [ABSTRACT FROM AUTHOR]