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ispartof: ANNALS OF STATISTICS vol:50 issue:5 pages:2973-3008 status: published

In this paper, we consider the statistical inference for the partially linear panel data models with fixed effects. We focus on the case where some covariates are measured with additive errors. We propose a modified profile least squares estimator of the regression parameter and the nonparametric components. The asymptotic normality for the parametric component and the rate of convergence for the nonparametric component are established. Consistent estimations of the error variance are also developed. We conduct simulation studies to demonstrate the finite sample performance of our proposed method and we also present an illustrative empirical application.

This article presents a novel total least-squares based method for errors-in-variables model identification with a known structure. This method considers the errors of both input and output variables and thus achieves more accurate estimates compared to conventional ordinary least-squares based methods.The introduced method consists of two recursive total least-squares algorithms connected in a hierarchical structure, which allows for exploitation of nuisance variables and a priori known structure of the identified model. The total least-squares (TLS) method is introduced, and a new "nuisance improved hierarchical total least-squares" (nHTLS) method is derived. Its properties are discussed and proved by simulations. Furthermore, the method is applied in a practical experiment consisting of the state-space identification of the permanent magnet synchronous motor (PMSM). The introduced method is compared with TLS and proven to provide measurably superior dynamical behavior and smaller estimation error of results.

Following the Guide to the expression of uncertainty in measurement (GUM), the slope and intercept in straight-line regression tasks can be estimated and their uncertainty evaluated by defining a measurement model. Minimizing the weighted total least-squares functional appropriately defines such a model when both regression input quantities ( X and Y ) are uncertain. This paper compares the uncertainty of the straight line evaluated by propagating distributions and by the law of propagation of uncertainty (LPU). The latter is in turn often approximated because the non-linear measurement model does not have closed form. We reason that the uncertainty recommended in the dedicated technical specification ISO/TS 28037:2010 does not fully implement the LPU (as intended) and can understate the uncertainty. A systematic simulation study quantifies this understatement and the circumstances where it becomes relevant. In contrast, the LPU uncertainty may often be appropriate. As a result, it is planned to revise ISO/TS 28037:2010.

This paper studies the measure of symmetry or asymmetry of a continuous variable under the multiplicative distortion measurement errors setting. The unobservable variable is distorted in a multiplicative fashion by an observed confounding variable. First, two direct plug-in estimation procedures are proposed, and the empirical likelihood based confidence intervals are constructed to measure the symmetry or asymmetry of 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 examined. 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.

Eyewitness identifications play a critical role in the investigation of crimes and the subsequent legal proceedings. However, law enforcement do not have the time and resources available to conduct the much-needed research for the development and validation of more reliable practices. Research in the effectiveness of law enforcement practices for eyewitness identification procedures remains incomplete. It is well known that eyewitnesses make errors, which often result in grievous consequences. Currently, there are a few options for eyewitness identification analysis, including receiver operating characteristic (ROC) curve analysis, Bayesian prior- posterior plots, and decision utility. All of these methods lack a fundamental way to include variability and the complex and interactive relationships of the variables affecting eyewitness identification accuracy. We will also discuss new methods for eyewitness identification (EWID) data, which are borrowed from fields such as diagnostic medicine. The tools and procedures for analyzing the data in meaningful and utilitarian ways from these fields can provide thoughtful and valid conclusions. Such methodologies require ease of use and interpretation, flexibility, and efficient implementation. This compilation of chapters shows the thought process involved in considering what kinds of methods and approaches to thinking could help lead to better EWID procedures, with the intention of resulting in fewer errors, both in false convictions and false acquittals. This research began with an interdisciplinary problem of understanding EWID data and existing statistical methodologies for the analysis of such data, as well as the consequences of an incomplete comprehension of the data. It was clear that there are latent variables to be estimated that are imperative to understand parts of the data, which resulted in the development of the proposed framework. This framework allows researchers to estimate an individual’s probability of accuracy, which is dependent on their individual probability of choosing a face from a lineup and the global probability of target presence in the lineup (i.e., base rate). The true value in the proposed method is how easily it is applied and interpreted, which could be helpful for law enforcement agents, lawyers, and jurors. A component of the estimation relies on the algorithm of random forests. Since EWID data is susceptible to measurement error due to the human component, we discovered that the impact of measurement error on random forest models needs further study. This thesis addresses that problem. The literature provides a frame- work for the asymptotic behavior of random forests. This provides the groundwork to derive an estimator for the mean difference of two random forest models. In our case, the random forest models are developed with and without measurement error to simulate the behaviors of the differences. In the simulations, it was clear that there is an effect from measurement error. Since measurement error is usually assumed to be nonexistent or negligible, this is a valuable finding. The next steps should be to develop a methodology similar to those already in place for classical statistical models to account for these errors.

Presentation on the comparison of errors-in-variables and marginalised errors-in-variables harmonisation methods given by R. Quast during the FIDUCEO science meeting at NPL in January 2019. This presentation supplements the journal article: Giering, R.; Quast, R.; Mittaz, J.P.D.; Hunt, S.E.; Harris, P.M.; Woolliams, E.R.; Merchant, C.J. A Novel Framework to Harmonise Satellite Data Series for Climate Applications. Remote Sens. 2019, 11, 1002. doi:10.3390/rs11091002., {"references":["Giering, R.; Quast, R.; Mittaz, J.P.D.; Hunt, S.E.; Harris, P.M.; Woolliams, E.R.; Merchant, C.J. A Novel Framework to Harmonise Satellite Data Series for Climate Applications. Remote Sens. 2019, 11, 1002"]}

This paper studies the linear dynamic errors-in-variables (EIV) problem in a fairly general condition where the input–output disturbing noises are colored and the input is quasi-stationary. A novel formulation of the extended frequency domain maximum likelihood (ML) estimator is developed which reduces the number of nonlinear normal equations to be solved. Sufficient conditions are provided to achieve local identifiability of the EIV model for specified noise cases of interest. The parameter estimates are calculated via a numerically stable Gauss–Newton minimization scheme started by an initial value generation strategy. Also, both the consistency and accuracy of the extended ML estimate are analyzed in detail. The performance of the proposed method is finally demonstrated on simulated dynamic systems.

Multiple imputation and maximum likelihood estimation (via the expectation- maximization algorithm) are two well-known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation-maximization approximation to the likelihood. In this thesis we show how these two methods are equivalent, and further, exploit this result to show that familiar likelihood-based approaches can be used to enhance multiple imputation’s performance in: (1) model selection, where familiar Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) can be used to choose the imputation model that best fits the observed data; (2) hypothesis testing, where the familiar likelihood-ratio statistic can be used to perform composite hypothesis testing with multiple imputed data; (3) measurement error modelling, where familiar functional methods, such as Simulation-extrapolation and Corrected score, can be used to account for measurement error with multiple imputed data. We verify these results empirically and demonstrate the use of the methods on several classical missing data examples.

Linkage analysis is a sophisticated media effect research design that reconstructs the likely exposure to relevant media messages of individual survey respondents by complementing the survey data with a content analysis. It is an important improvement over survey-only designs: Instead of predicting some outcome of interest by media use and implicitly assuming what kind of media messages the respondents were exposed to, linkage analysis explicitly takes the media messages into account (de Vreese & Neijens, 2016; Scharkow & Bachl, 2017; Schuck, Vliegenthart, & de Vreese, 2016; Shoemaker & Reese, 1990; Slater, 2016; Valkenburg & Peter, 2013). The design in its modern form has been pioneered by Miller, Goldenberg, and Erbring (1979) and is today considered a “state-of-the art analysis of the impact of specific news consumption” (Fazekas & Larsen, 2015, p. 196). Its widespread use, especially in the field of political communication, and its still increasing popularity demonstrate the relevance of the design. The main advantage of a linkage analysis is the use of one or more message exposure variables which combine information about media use and media content. However, both constitutive sources are often measured with error: Survey respondents are not very good at reporting their media use reliably, and coders will often make some errors when classifying the relevant messages.In this article, we will first give a short overview on the prevalence and consequences of measurement error in both data sources. The arguments are based on a literature review and a simulation study which are published elsewhere in full detail (Scharkow & Bachl, 2017). We continue with a discussion of possible remedies in measurement and data analysis. Beyond the obvious need to improve the measures themselves, we highlight the importance of serious diagnostics of measurement quality. Such information can then be incorporated in the data analysis using estimation or imputation approaches, which are introduced in the main section of this chapter. We conclude by noting that 1) the improvement of measurements and the diagnosis of measurement error in both parts of a linkage analysis must be taken seriously; 2) many tools for correcting measurement error in single parts of a linkage analysis already exist and should be used; 3) methodological research is needed for the development of an integrated analysis workflow which accounts for measurement error and uncertainty in both data sources.

In this paper, we propose a non-iterative direct data-driven control approach, such that the controller is directly identified from input/output data without plant identification step. First we formulate the problem of designing a controller in order to match the behavior of an assigned reference model in terms of an equivalent set-membership errors-in-variables problem and we define the feasible controller parameter set. Then, we design the controller parameters by applying previous results by the authors in the field of convex relaxation for errors-in-variables identification. Finally, the effectiveness of the presented technique is shown by means of two simulated examples.

Peter Hall died in Melbourne on January 9, 2016. He was an extremely prolific researcher and contributed to many different areas of statistics. In this paper, I talk about my experience with Peter and I summarise his main contributions to deconvolution, which include measurement error problems and problems in image analysis.

Frequency response function (FRF) measurements are very often used to get a quick insight into the dynamic behavior of complex systems; even if it is known that these systems are only approximately linear and time-invariant. Therefore, it is important to detect and quantify the deviation from the ideal linear time-invariant framework that is inherent to the concept of an FRF. This paper presents a method to detect and quantify the nonlinear and time-variant effects in FRF measurements using periodic excitations. The proposed method can handle noisy input, noisy output data, and nonlinear time-variant systems operating in feedback.

The steady state response of a system to a periodic input is still subject to noise transients. For lightly damped systems these noise transients can significantly increase the variance of the estimated frequency response function (FRF). This paper presents a method that suppresses the influence of the noise transients (leakage errors) in nonparametric FRF and noise (co-)variance estimates of dynamic systems excited by periodic signals. The method is based on a local polynomial approximation of the noise leakage errors on the FRF. Compared with the classical approaches, the proposed procedure is more robust and needs less measurement time (two signal periods are sufficient). The theory is supported by simulation and real measurement examples.

This paper presents an extension of the well known linear time invariant identification theory to Linear, Periodically Time-Varying (LPTV) systems. The considered class of systems is described by ordinary differential equations with coefficients that vary periodically over time, making use of multisines both for excitations as well as for the time-varying system parameters. To solve the model equation, an efficient frequency domain simulator is built and is compared with the classically time integration solvers. Further, a frequency domain identification algorithm is proposed within an errors-in-variables stochastic framework. This approach determines a parametric model for the LPTV-system from noisy input-output data. The developed estimation theory is also verified on a simulation example.

This paper considers the parametric identification of single-input single-output, linear, discrete-time, time-varying systems. The model equation is a linear ordinary difference equation with coefficients varying as polynomials in time. The model equation is formulated exactly in the frequency domain. Based on this equation a consistent estimator is constructed within an errors-in-variables framework. The estimator is illustrated on a simulation example.

Cataloged from PDF version of article. A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values.

This is Part II of a series of two papers on the estimation of nonparametric noise and frequency response function models for multiple input, multiple output systems excited by arbitrary inputs. Part I (Pintelon et al. (2009)) [1] develops the methodology for linear dynamic multivariable systems with exactly known input and where the output is disturbed by stationary noise ( = output error problem ) . The contributions of Part II are the following. First, it is shown that the proposed method can be used for nonlinear systems and for parametric identification of the system dynamics in a generalized output error framework. Next, the methodology is generalized to handle noisy input–output data ( = errors -in-variables problem), and identification in feedback. Finally, the approach is illustrated on simulations and real measurements examples.

Magnetotelluric (MT) surveying is an Electromagnetic (EM) surveying technique used in geophysics and mineral exploration. The main problem in MT surveying is the estimation of the impedance of the ground, which is obtained as the ratio between the natural environmental electric and magnetic fields measured on the surface of the target area. Because these measurements are inherently corrupted by noise, the impedance estimate may be biased (Errors-In-Variables (EIV)), which is a difficulty well-known in MT literature and typically overcome by the use of additional independent measurements. This paper formulates the MT problem as a standard system identification problem, and uses output-error model structures to obtain scalar (SISO) and vector (TISO) ground impedance estimates. Estimation bias is minimised by selecting segments of data with high Signal-to-Noise Ratio (SNR). The SISO and TISO modelling approaches are discussed and compared on results obtained from experimental MT data.

ARMAX models constitute an excellent compromise between performance and complexity and can model in an effective way the presence of disturbances acting on the process state. These models, however, do not take into account the observation errors on the output of the process to be identified and this can be particularly important in applications like filtering and fault diagnosis. This paper concerns extended ARMAX models that consider also the presence of additive white noise on the output observation and describes an approach for their identification that takes advantage of both the errors–in–variables framework and the instrumental variable properties. The paper reports also the results of Monte Carlo simulations that underline the effectiveness of the proposed approach.

International audience; This paper deals with identification of dynamic discrete-time errors-in-variables systems. The statistical accuracy of a least squares estimator based on third-order cumulants is analyzed. In particular, the asymptotic covariance matrix of the estimated parameters is derived. The results are supported by numerical simulation studies.

Summary We consider quadratic regression models where the explanatory variable is measured with error. The effect of classical measurement error is to flatten the curvature of the estimated function. The effect on the observed turning point depends on the location of the true turning point relative to the population mean of the true predictor. Two methods for adjusting parameter estimates for the measurement error are compared. First, two versions of regression calibration estimation are considered. This approximates the model between the observed variables using the moments of the true explanatory variable given its surrogate measurement. For certain models an expanded regression calibration approximation is exact. The second approach uses moment-based methods which require no assumptions about the distribution of the covariates measured with error. The estimates are compared in a simulation study, and used to examine the sensitivity to measurement error in models relating income inequality to the level of economic development. The simulations indicate that the expanded regression calibration estimator dominates the other estimators when its distributional assumptions are satisfied. When they fail, a smallsample modification of the method-of-moments estimator performs best. Both estimators are sensitive to misspecification of the measurement error model.

We consider the problem of estimating the support of a multivariate density based on contaminated data. We introduce an estimator, which achieves consistency under weak conditions on the target density and its support, respecting the assumption of a known error density. Especially, no smoothness or sharpness assumptions are needed for the target density. Furthermore, we derive an iterative and easily computable modification of our estimation and study its rates of convergence in a special case; a numerical simulation is given.

International audience; A novel direct approach for identifying continuous-time linear dynamic errors-in-variables models is presented in this paper. The effects of the noise on the state-variable filter outputs are analyzed. Subsequently, a few algorithms to obtain consistent continuous-time parameter estimates in the errors-in-variables framework are derived. It is also possible to design search-free algorithms within our framework. The algorithms can be used for nonuniformly sampled data. The asymptotic distributions of the estimates are derived. The performances of the proposed algorithms are illustrated with some numerical simulation examples.

Estimation problems for linear time-invariant systems with noisy input and output are considered. The smoothing problem is a least norm problem. An efficient algorithm using a Riccati-type recursion is derived. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate. The result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem.

This paper proposes a constrained empirical likelihood confidence region for a parameter β0 in the linear errors-in-variables model: Yi = xiτβ0 + ei,Xi, = xi + ui,(1≤i≤n), which is constructed by combining the score function corresponding to the squared orthogonal distance with a constrained region of β0. It is shown that the coverage error of the confidence region is of order n-1, and Bartlett corrections can reduce the coverage errors to n-2. An empirical Bartlett correction is given for practical implementation. Simulations show that the proposed confidence region has satisfactory coverage not only for large samples, but also for small to medium samples.

We present a novel method for estimating physical properties of an underground hydrocarbon reservoir, on the basis of generally measured wellbore ow rate and pressure signals at the bottom of a producing well. The method uses instrumental variable-based system identification techniques to solve for a closed-loop errors-in-variables problem. It is different from the conventional methods as it allows the instrumental variable signal to be correlated with the input and output signals' noise. This property increases the number of possible candidates to be used as the instrumental variable signal. The application of the proposed method has been investigated on a synthetic case study.

We consider estimation and confidence regions for the parametersαandβbased on the observations (X1, Y1), …, (Xn, Yn) in the errors-in-variables modelXi=Zi+eiandYi=α+βZi+fifor normal errorseiandfiof which the covariance matrix is known up to a constant. We study the asymptotic performance of the estimators defined as the maximum likelihood estimator under the assumption thatZ1, …, Znis a random sample from a completely unknown distribution. These estimators are shown to be asymptotically efficient in the semi-parametric sense if this assumption is valid. These estimators are shown to be asymptotically normal even in the case thatZ1, Z2, … are arbitrary constants satisfying a moment condition. Similarly we study the confidence regions obtained from the likelihood ratio statistic for the mixture model and show that these are asymptotically consistent both in the mixture case and in the case thatZ1, Z2, … are arbitrary constants.

The problem of fitting a parametric model in Tobit errors-in-variables regression models is discussed in this paper. The proposed test is based on the supremum of the Khmaladze type transformation of a certain partial sum process of calibrated residuals. This framework covers the usual error-free Tobit model as a special case. The asymptotic null distribution of this transformed process is shown to be the same as that of a time transformed standard Brownian motion. Consistency against some fixed alternatives and asymptotic power under some local nonparametric alternatives of this test are also discussed. Simulation studies are conducted to assess the finite sample performance of the proposed test.

The problem introduced by grouping income data when measuring socioeconomic inequalities in health (and health care) has been highlighted in a recent study. We reexamine 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 bias results from 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 compare the performance of these methods using data from 15 European countries and the United States. 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.

In various applications from radar processing to mobile communication systems based on CDMA or OFDM, M-AR multichannel processes are often considered and may be combined with Kalman filtering. However, the estimations of the M-AR parameter matrices and the autocorrelation matrices of the additive noise and the driving process from noisy observations are key problems to be addressed. In this paper, we suggest solving them as an errors-in-variables issue. In that case, the noisy-observation autocorrelation matrix compensated by a specific diagonal block matrix and whose kernel is defined by the M-AR parameter matrices must be positive semi-definite. Hence, the parameter estimation consists in searching every diagonal block matrix that satisfies this property, in reiterating this search for a higher model order and then in extracting the solution that belongs to both sets. A comparative study is then carried out with existing methods including those based on the Extended Kalman Filter (EKF) and the Sigma-Point Kalman Filters (SPKF). It illustrates the relevance and advantages of the proposed approaches.

We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while one has available a sample $(W_1,Y_1),...,(W_n,Y_n)$ of independent and identically distributed data, representing observations with precisely measured predictors, where $\mathrm{E}(Y_i|W_i)=g(W_i)$, instead of the smooth regression function $g$, the target of interest is another smooth regression function $m$ that pertains to predictors $X_i$ that are noisy versions of the $W_i$. Our target is then the regression function $m(x)=E(Y|X=x)$, where $X$ is a contaminated version of $W$, that is, $X=W+\delta$. It is assumed that either the density of the errors is known, or replicated data are available resembling, but not necessarily the same as, the variables $X$. In either case, and under suitable conditions, we obtain $\sqrt{n}$-rates of convergence of the proposed estimator and its derivatives, and establish a functional limit theorem. Weak convergence to a Gaussian limit process implies pointwise and uniform confidence intervals and $\sqrt{n}$-consistent estimators of extrema and zeros of $m$. It is shown that these results are preserved under more general models in which $X$ is determined by an explanatory variable. Finite sample performance is investigated in simulations and illustrated by a real data example., Comment: Published in at http://dx.doi.org/10.1214/009053607000000497 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

In many economic applications, observations are naturally categorized into mutually exclusive and exhaustive groups. For example, individuals can be classified into cohorts and workers are employees of a particular firm. Grouping models are widely used in economics -- for example, cohort models have been used to study labour supply, wage inequality, consumption, and intergenerational transfer of human capital. The simplest grouping estimator involves taking the means of all variables for each group and then carrying out a group-level regression by OLS or weighted least squares. This estimator is biased in finite samples. I show that the standard errors in variables estimator (EVE) designed to correct for small sample bias is exactly equivalent to the Jack-knife Instrumental Variables Estimator (JIVE). Also EVE is closely related to the k-class of instrumental variables estimators. I then use results from the instrumental variables literature to develop an estimator (UEVE) with better finite-sample properties than existing errors in variables estimators. The theoretical results are demonstrated using Monte Carlo experiments. Finally, I use the estimators to implement a model of inter-temporal male labour supply using micro data from the United States Census. There are sizeable differences in the wage elasticity across estimators, showing the practical importance of the theoretical issues discussed in this paper even in circumstances where the sample size is quite large.

This study explores a new modelling approach that bridges the gap between multilateral country-level data and the bilateral-model based, goods-market specific purchasing power parity (PPP) hypothesis. Under this approach, PPP is embedded in latent common factors, extractable from a large set of bilateral price disparities, and tested via an error-correction model where the factors act as error-correction leading indicators for exchange rate and inflation. Significant modelling results for five OECD countries using monthly data suggest that the extant finding of insignificant PPP using similar data should be due to errors-invariables attenuation and that its correction lies in effective construction of latent variables.

This paper deals with the identification of time-varying frequency-flat Rayleigh fading channels disturbed by an additive white Gaussian noise, using a training sequence based approach. When the channel is modeled by an Autoregressive (AR) process, it can be estimated by using a Kalman filter. However, this solution requires the preliminary unbiased estimations of the AR parameters and the variances of both the additive noise and the driving process in the state space representation of the system. Instead of using the existing noise compensated approaches which usually require a long observation window and do not necessarily provide reliable estimates when the signal to noise ratio is low, we propose an alternative approach using recent results developed for the Errors-In-Variables (EIV) issue. This method consists in estimating the kernel of specific autocorrelation matrices and has the advantage of providing both the noise variances and the channel AR parameters. Moreover, the maximum Doppler frequency can be also deduced.

We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+\xi, \; Z=X+\sigma\varepsilon$, involving independent and unobserved random variables $X,\xi,\varepsilon$. The density $g$ of $X$ is unknown, whereas the density of $\sigma\varepsilon$ is completely known. Using the observations $(Y_i, Z_i)$, $i=1,\cdots,n$, we propose an estimator of the regression function $f$, built as the ratio of two penalized minimum contrast estimators of $\ell=fg$ and $g$, without any prior knowledge on their smoothness. We prove that its $\mathbb{L}_2$-risk on a compact set is bounded by the sum of the two $\mathbb{L}_2(\mathbb{R})$-risks of the estimators of $\ell$ and $g$, and give the rate of convergence of such estimators for various smoothness classes for $\ell$ and $g$, when the errors $\varepsilon$ are either ordinary smooth or super smooth. The resulting rate is optimal in a minimax sense in all cases where lower bounds are available.

It is well known that consistent estimators of errors-in-variables models require knowledge of the ratio of error variances. What is not well known is that a Joint Least Squares estimator is robust to a wide misspecification of that ratio. Through a series of Monte Carlo experiments we show that an easy-to-implement estimator produces estimates that are nearly unbiased for a wide range of the ratio of error variances. These MC analyses encompass linear and nonlinear specifications and also a system on nonlinear equations where all the variables are measured with errors.

SIMEX was introduced by Cook and Stefanski (1994) as a simulation type estimator in errors-in-variables models. The idea of the SIMEX procedure is to compensate for the effect of the measurement errors while still using naive regression estimators. Polzehl and Zwanzig (2004) defined a symmetrized version of this estimator. In this paper we establish some results relating these two simulation-extrapolation-type estimators to well known consistent estimators like the total least squares estimator (TLS) and the moment estimator (MME) in the context of errors-in-variables models. We further introduce an adaptive SIMEX (ASIMEX), which is calculated like SIMEX, but based on an estimated variance. The main result of this paper is that SYMEX, ASIMEX are equivalent to TLS. Additionally we see that SIMEX is equivalent to the moment estimator.

The consequences of errors in trade classification are potentially worse than documented in existing empirical research. This is demonstrated by the use of a formal model of classification errors in a generic regression-type microstructure model. The bias is a function of the probability of trade-reversal in addition to the probability of an error. These parameters depend on stock and trade characteristics in addition to trading procedures and trade reporting standards. The bias is highly sensitive to the background variables, thus causing concern about the validity of empirical studies applying possibly erroneous classification methods without controlling for such effects. The theory, outlined in the paper, predicts that given empirical evidence on error rates, effective spreads must realistically be expected to be downward biased by more than 50%. However, the bias one can observe from using the TORQ database is less severe and has the opposite sign. This is due to special features of the NYSE trading process which may not carry over to other markets. This research also emphasizes the need for proper adjustment of classification error bias. Therefore, the paper proposes a GMM estimator for improved estimation. Simulation evidence indicates that in medium and larger sized samples the method is capable of removing virtually all the bias in market quality statistics like e¤ective, realized, and adverse selection spreads. This is empirically verified in an application to data from TORQ.

Techniques for the analysis of spatial data have, to date, tended to ignore any effect caused by error in specifying the spatial locations at which measurements are recorded. This paper reviews the methods for adjusting spatial inference in the presence of data-location error, particularly for data that have a continuous spatial index (geostatistical data). New kriging equations are developed and evaluated based on a simulation experiment. They are also applied to remote-sensing data from the Total Ozone Mapping Spectrometer instrument on the Nimbus-7 satellite, where the location error is caused by assignment of the data to their nearest grid-cell centers. The remote-sensing data measure total column ozone (TCO), which is important for protecting the Earth's surface from ultraviolet and other radiation.

In this paper we develop a simple maximum likelihood estimator for probit models where the regressors have measurement error. We first assume precise information about the reliability ratios (or, equivalently, the proxy correlations) of the regressors. We then show how reasonable bounds for the parameter estimates can be obtained when only imprecise information is available. The analysis is also extended to situations where the measurement error has non-zero mean and is correlated with the true values of the regressors. An extensive simulation study shows that the estimator works very well, even in quite small samples. Finally the method is applied to data explaining sick leave in Sweden.

The axiomatic literature on technical efficiency measurement has drawn attention to the indication problem of the Debreu-Farrell (DF) measure. We follow a shadow price approach to preserve the DF benchmark while reconciling it with the Koopmans efficiency characterization. First, we define a set of Koopmans efficient references that can be rationalized in a similar way as the DF projection. The indication problem is then captured using a measure of implicit allocative or mix efficiency, also interpretable as a dominance measure in price space. We consequently present a mix-adjusted DF framework for efficiency measurement in which e.g. the Zieschang (1984) procedure can be

This paper develops a procedure for estimating parameters of a cross-sectional stochastic frontier production function when the factors of production suffer from measurement errors. Specifically, we use Fuller's (1987) reliability ratio concept to develop an estimator for the model in Aigner et al (1977). Our Monte-Carlo simulation exercise illustrates the direction and the severity of bias in the estimates of the elasticity parameters and the returns to scale feature of the production function when using the traditional maximum-likelihood estimator (MLE) in presence of measurement errors. In contrast the reliability ratio based estimator consistently estimates these parameters even under extreme degree of measurement errors. Additionally, estimates of firm level technical efficiency are severely biased for traditional MLE compared to reliability ratio estimator, rendering inter-firm efficiency comparisons infeasible. The seriousness of measurement errors in a practical setting is demonstrated by using data for a cross-section of publicly traded U.S. corporations.

General Method of Moments (GMM) estimation of a linear one-equation model using panel data with errors-in-variables is considered. To eliminate fixed individual heterogeneity, the equation is differenced across one or more than one periods and estimated by means of instrumental variables. With non-autocorrelated measurement error, we show that only the one-period and a few two-period differences are essential, i.e. relevant for GMM-estimation. GMM estimation based on all orthogonality conditions on the basis of a generalized inverse formulation is shown to be equivalent to estimation using only the essential orthogonality conditions

The problem of constructing confidence sets for the structural errors-in-variables model is considered under the assumption that the variance of the error associated with the covariate is known. Previously proposed confidence sets for this model suffer from the problem that they all have zero confidence levels for any sample size, where the confidence level of a confidence set is defined to be the infimum of coverage probability over the parameter space. In this paper we construct some asymptotically honest confidence sets; that is, the limiting values of their confidence levels are at least as large as the nominal probabilities when the sample size goes to $\infty$. A desirable property of the proposed confidence set for the slope is also established.

We consider a semiparametric estimation method for general regression models when some of the predictors are measured with error. The technique relies on a kernel regression of the "true" covariate on all the observed covariates and surrogates. This requires a nonparametric regression in as many dimensions as there are covariates and surrogates. The usual theory copes with such higher-dimensional problems by using higher-order kernels, but this is unrealistic for most problems. We show that the usual theory is essentially as good as one can do with this technique. Instead of regression with higher-order kernels, we propose the use of dimension reduction techniques. We assume that the "true" covariate depends only on a linear combination of the observed covariates and surrogates. If this linear combination were known, we could apply the one-dimensional versions of the semiparametric problem, for which standard kernels are applicable. We show that if one can estimate the linear directions at the root-$n$ rate, then asymptotically the resulting estimator of the parameters in the main regression model behaves as if the linear combination were known. Simulations lend some credence to the asymptotic results.

This paper examines panel data modelling with latent variables in analyzing log-linear relations between inputs and output of firms. Our particular focus is on (i) the "increasing returns to scale puzzle" for labour input and (ii) the GMM estimation in the context of errors-in-variables and panel data. The IV's used for the observed log-differenced output are log output (in level form) for other years than those to which the difference(s) refer. Flexible assumptions are made about the second order moments of the errors, the random coefficients, and other latent variables, allowing, inter alia, for arbitrary heteroskedasticity and autocorrelation up to the first order of the errors-in-variables. We compare OLS, 2SLS, and GMM estimates of the average input response elasticity (which in some cases can be interpreted as an average inverse scale elasticity), and investigate whether year specific estimates differ substantially from those obtained when data for all years are combined. The results confirm the "increasing returns to scale puzzle" for labour input (measured in three different ways), but indicate approximately constant returns to scale when we consider the material input response. This indicates non-homotheticity of the production technology.

We examine estimation of a model of producer behavior in the presence of correlated measurement errors in the regressors. Scale economies and price-cost margins are estimated from a set of panel data for manufacturing plants. The paper presents a somewhat new model for estimation of these parameters which is highly flexible but with a simple regression structure. Perhaps the most important contribution of the paper is some new results on deriving parameter bounds for a regression model with errors in variables. In particular, we consider the case where the measurement errors might be correlated. We derive asymptotic standard errors for the parameter bounds. These asymptotic standard errors are compared to bootstrap estimates. Our new results on parameter bounds are applied to the estimation of the model of producer behavior.

Consider a generalized linear model with response $Y$ and scalar predictor $X$. Instead of observing $X$, a surrogate $W = X + Z$ is observed, where $Z$ represents measurement error and is independent of $X$ and $Y$. The efficient score test for the absence of association depends on $m(w) = E(X\mid W = w)$ which is generally unknown. Assuming that the distribution of $Z$ is known, asymptotically efficient tests are constructed using nonparametric estimators of $m(w)$. Rates of convergence for the estimator of $m(w)$ are established in the course of proving efficiency of the proposed test.

The usual assumption in the classical errors-in-variables problem of independent measurement errors cannot necessarily be maintained when the data are time series; errors may be strongly serially correlated, possibly containing seasonal effects and trends. When it is possible to identify frequency bands over which the signal-to-noise ratio is large, an approximate solution to the errors-in-variables problem is to omit the remaining frequencies from a time series regression. We draw attention to the danger of “leakage” from the omitted frequencies, and show that the consequent bias can be reduced by means of tapering.