Measurement Error Variance Research Articles

A Bayesian space‐time analysis of acid deposition data combined from two monitoring networks

In some studies of atmospheric pollution, deposition data may be available from several distinct monitoring networks. Systematic differences may exist between networks, and an effective statistical analysis of the data combined from all networks should account for this possibility. This article develops a Bayesian modeling approach for spatiotemporal data from two monitoring networks that accounts for possible network differences in measurement error biases and variances. Wet sulfate deposition data from two networks in the eastern United States, the National Acid Deposition Program/National Trends Network and the Clean Air Status and Trends Network, are combined and analyzed via our modeling approach. We examine whether the temporal trend in deposition from 1989–1997 varies regionally and whether the measurement error biases and variances differ between networks. We also demonstrate how prediction uncertainty is reduced using the combined data from levels obtained when basing prediction on data from only one of the networks.

Relative efficiency of three estimators in a polynomial regression with measurement errors

In a polynomial regression with measurement errors in the covariate, the latter being supposed to be normally distributed, one has (at least) three ways to estimate the unknown regression parameters: one can apply ordinary least squares (OLS) to the model without regard to the measurement error or one can correct for the measurement error, either by correcting the estimating equation (ALS) or by correcting the mean and variance functions of the dependent variable, which is done by conditioning on the observable, error ridden, counter part of the covariate (SLS). While OLS is biased, the other two estimators are consistent. Their asymptotic covariance matrices and thus their relative efficiencies can be compared to each other, in particular for the case of a small measurement error variance. In this case, it appears that ALS and SLS become almost equally efficient, even when they differ noticeably from OLS.

An Evaluation of the Reliability of Accounting Based Measures of Expected Returns: A Measurement Error Perspective

We develop and implement a method for comparing the measurement error in estimates of the expected rate of return on equity. We combine the Campbell [1991] and Vuolteenaho [2002] return decomposition with the econometric method described in Garber and Klepper [1980] and Barth [1991] to infer cross-sectional measurement error variances. We evaluate a variety of estimates of expected returns that are discussed in the extant accounting literature (e.g., Gebhardt, Lee, and Swaminathan [2001], Easton [2002], and Gode and Mohanram [2002]). Our results show that the estimate that is based on the simplest model (i.e., price-to-forward earnings) is as reliable as more sophisticated proxies. This result is also observed when the analyses are repeated for portfolios of observations. Predicted values based on instrumental variables that are, a priori, expected to be correlated with the true expected return but uncorrelated with the measurement error have considerably lower measurement error variances. Nonetheless, the crudest proxy still performs at least as well as more sophisticated proxies.

Scope for a random regression model in genetic evaluation of beef cattle for growth

Potential improvement in accuracy of genetic evaluation of beef cattle for growth from replacing the current multi-trait (MT) model comprising birth, weaning, yearling and final weights as separate traits, with a random regression (RR) model analysis is examined by simulation. Maintaining the original data and pedigree structure for three beef cattle data sets, data were simulated assuming a cubic regression on polynomials of age for direct and maternal, genetic and permanent environmental effects and heterogeneous measurement error variances. Ages at weighing from birth to 730 days were considered. Data set I represented records from an experimental herd with monthly weighing of animals. Data sets II and III were field data, selecting a subset of herds in which at least 50% of animals had four or more weights recorded and records for all herds for a small breed, respectively. Simulated records were analysed fitting a MT model and RR models. Field data sets were expanded by adding a fictitious weight approximately 3 months after the original records. Accuracy of genetic evaluation was calculated as correlation between true and estimated values for each analysis. For the same subset of data, accuracies from a RR analysis were consistently higher than for a MT analysis, due to more appropriate modelling of variances and genetic parameters. Using all records available, RR accuracies for breeding value estimates for 200, 400 and 600 days in data set I were 0.023–0.034 or 4.3–5.9% higher than for MT. Corresponding gains were 3.1–3.6% for data set II and 1.5–1.7% for data set III. Expanding the field data sets by 100%, increased RR accuracies by 0.027–0.038 over those from MT analyses. While small in absolute terms, this was equivalent to a proportional increase of 5.7–8.3%. Results showed that substantial benefits could be obtained from the implementation of a RR model, if additional weight records were collected.

The efficiency of adjusted least squares in the linear functional relationship

A linear functional errors-in-variables model with unknown slope parameter and Gaussian errors is considered. The measurement error variance is supposed to be known, while the variance of errors in the equation is unknown. In this model a risk bound of asymptotic minimax type for arbitrary estimators is established. The bound lies above that one which was found previously in the case of both variances known. The bound is attained by an adjusted least-squares estimators.

Preliminary test estimators of the parameters of simple linear model with measurement error

In this paper, we discuss the properties of preliminary test estimators (PTE) of the parameters of simple linear model with measurement error (ME model) when the slope of the linear model is suspected to be zero. Expressions of the bias, MSE and efficiencies are obtained under conditional as well as unconditional situations with known reliability coefficient. Conditional model results are compared to the standard model without measurement error. We also provide the unconditional model analysis in finite samples. Asymptotic theory under local alternatives is developed when the variance of measurement error or the ratio of the variance of the model error relative to the variance of the measurement error is known. Asymptotic expressions of bias and MSE of the estimators along with their efficiencies are obtained. In every case, it is shown that the measurement error tend to increase the variability of the estimators compared to the estimators without measurement error. Graphs and tables are provided to see these results and to determine optimum level of significance for minimum guaranteed efficiency.

Impact of measurement errors in stochastic inverse conditional modelling by the self-calibrating approach

A synthetic study is presented analyzing the impact of measurement errors on transmissivity and/or hydraulic head in the stochastic inverse modeling of groundwater flow, using the sequential self calibrated method. The scenarios studied can be divided into two different groups: (1) The modeler assumes the data are error-free when they are not; the attempt to reproduce these erroneous data yields biases and artifacts in the final conditional models. (2) The modeler recognizes that the data have measurement errors, makes an estimation of their magnitude, and accounts for them in the simulation; there are no biases or artifacts in this case, just an increase in the uncertainty about the final conditional models. The impact of the errors is analyzed in terms of the ensemble means and variances of the conditional realizations of transmissivity and the ensemble means and variances of the resulting hydraulic head fields after solution of the flow equation in the conditional transmissivity realizations. For the cases analyzed here, both transmissivity and head errors yield a worse characterization of the flow situation and transmissivity errors are less important than errors on hydraulic head for estimating the hydraulic head field. The characterization of the hydraulic head and transmissivity reference fields is better when the modeler estimates correctly the measurement error variance and takes into account the measurement errors in the modeling as outlined in the paper. In case the erroneous transmissivity data are treated as error-free, the ensemble standard deviation of transmissivity becomes unrealistic low. The synthetic study does not clearly reveal the existence of an interaction between hydraulic head measurement errors and transmissivity measurement errors; the effect of the errors seems to be additive.

The quality of volatility traded on the over‐the‐counter currency market: A multiple horizons study

AbstractPrevious studies of the quality of market‐forecasted volatility have used the volatility that is implied by exchange‐traded option prices. The use of implied volatility in estimating the market view of future volatility has suffered from variable measurement errors, such as the non‐synchronization of option and underlying asset prices, the expiration‐day effect, and the volatility smile effect. This study circumvents these problems by using the quoted implied volatility from the over‐the‐counter (OTC) currency option market, in which traders quote prices in terms of volatility. Furthermore, the OTC currency options have daily quotes for standard maturities, which allows the study to look at the market's ability to forecast future volatility for different horizons. The study finds that quoted implied volatility subsumes the information content of historically based forecasts at shorter horizons, and the former is as good as the latter at longer horizons. These results are consistent with the argument that measurement errors have a substantial effect on the implied volatility estimator and the quality of the inferences that are based on it. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:261–285, 2003

Maximum Likelihood Estimation of Generalized Linear Models with Covariate Measurement Error

Generalized linear models with covariate measurement error can be estimated by maximum likelihood using gllamm, a program that fits a large class of multilevel latent variable models (Rabe-Hesketh, Skrondal, and Pickles 2004). The program uses adaptive quadrature to evaluate the log likelihood, produc- ing more reliable results than many other methods (Rabe-Hesketh, Skrondal, and Pickles 2002). For a single covariate measured with error (assuming a classical measurement model), we describe a "wrapper" command, cme, that calls gllamm to estimate the model. The wrapper makes life easy for the user by accepting a simple syntax and data structure and producing extended and easily interpretable output. The commands for preparing the data and running gllamm can also be obtained from cme. We first discuss the case where several measurements are avail- able and subsequently consider estimation when the measurement error variance is instead assumed known. The latter approach is useful for sensitivity analy- sis assessing the impact of assuming perfectly measured covariates in generalized linear models. An advantage of using gllamm directly is that the classical co- variate measurement error model can be extended in various ways. For instance, we can use nonparametric maximum likelihood estimation (NPMLE) to relax the normality assumption for the true covariate. We can also specify a congeneric measurement model which relaxes the assumption that the measurements for a unit are exchangeable replicates by allowing for different measurement scales and error variances.

誤差重み付けによる３次元復元形状の補正法

this paper proposes a new method for iteratively correcting three dimensional (3-d) shapes by weighting reconstruction errors when the shape is reconstructed from more than three 2-d perspective images using linear camera models such as weak-or para-perspective cameras. the method can compensate measurement errors by using its variance-covariance matrix, where the measurement errors are composed of random noise and the disparity between the linear camera models and non-linearity of perspective cameras, and can reduce mean reconstruction errors by adjusting the tolerance range of the reconstruction errors in accordance with the measurement error variances and also by eliminating the covariances between these errors. in numerical experiments using synthetic and real images, our method achieves correction results that are almost equivalent to those obtained by using variance-covariance matrices determined by a precise 3-d shape. the method also achieves a considerable amount of correction for both essentially nonlinear camera images and approximately linear camera images if the random noise is not strong and if more than twenty 2-d images are available.

Generalized Method of Moments Estimation When a Parameter Is on a Boundary

This article establishes the asymptotic distributions of generalized method of moments (GMM) estimators when the true parameter lies on the boundary of the parameter space. The conditions allow the estimator objective function to be nonsmooth and to depend on preliminary estimators. The boundary of the parameter space may be curved and/or kinked. The article discusses three examples: (1) instrumental variables (IV) estimation of a regression model with nonlinear equality and/or inequality restrictions on the parameters; (2) method of simulated moments estimation of a multinomial discrete response model with some random coefficient variances equal to 0, some random effect variances equal to 0, or some measurement error variances equal to 0; and (3) semiparametric least squares estimation of a partially linear regression model with nonlinear equality and/or inequality restrictions on the parameters.

Empirical simulation extrapolation for measurement error models with replicate measurements

We present a variation of the simex algorithm (J. Amer. statist. Assoc. 89 (1994) 1314) appropriate for the case in which the measurement error variance(s) are unknown but replicate measurements are available. The method used pseudo errors generated from random linear contrasts of the observed replicate measurements. An attractive feature of the new method is its ability to accommodate heteroscedastic measurement error.

Myers-Briggs Type Indicator Score Reliability Across: Studies a Meta-Analytic Reliability Generalization Study

The Myers-Briggs Type Indicator (MBTI) was submitted to a descriptive reliability generalization (RG) analysis to characterize the variability of measurement error in MBTI scores across administrations. In general, the MBTI and its scales yielded scores with strong internal consistency and test-retest reliability estimates, although variation was observed.

Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography.

A method for inverting measurements made on the surfaces of tissues for recovery of interior optical property maps is demonstrated for sparse near-infrared (NIR) fluorescence measurement sets on large tissue-simulating volumes with highly variable signal-to-noise ratio. A Bayesian minimum-variance reconstruction algorithm compensates for the spatial variability in signal-to-noise ratio that must be expected to occur in actual NIR contrast-enhanced diagnostic medical imaging. Image reconstruction is demonstrated by using frequency-domain photon migration measurements on 256-cm(3) tissue-mimicking phantoms containing none, one, or two 1-cm(3) heterogeneities with 50- to 100-fold greater concentration of Indocyanine Green dye over background levels. The spatial parameter estimate of absorption owing to the dye was reconstructed from only 160 to 296 surface measurements of emission light at 830 nm in response to incident 785-nm excitation light modulated at 100 MHz. Measurement error of acquired fluence at fluorescent emission wavelengths is shown to be highly variable. Convergence and quality of image reconstructions are improved by Bayesian conditioning incorporating (i) experimentally determined measurement error variance, (ii) recursively updated estimates of parameter uncertainty, and (iii) dynamic zonation. The results demonstrate that, to employ NIR fluorescence-enhanced optical imaging for large volumes, reconstruction approaches must account for the large range of signal-to-noise ratio associated with the measurements.

Occupational Stratification across the Life Course: Evidence from the Wisconsin Longitudinal Study

Sociologists frequently study changes across cohorts in the consequences of family background, gender, education, and cognitive ability for occupational outcomes. This study focuses, however, on how the consequences of these variables change within the course of individuals’ lives. To appropriately estimate changes across the life course in the determinants of occupational standing, corrections are made for measurement errors in variables, and data on siblings are used to account for all aspects (measured and unmeasured) of family background. The analyses use data from the Wisconsin Longitudinal Study, which provides multiple measures of siblings’ occupational standing at four points in their lives. Models of sibling resemblance show that the effects of family background on occupational standing operate entirely through their effects on education and cognitive ability. The effects of education decline across the life course, while the effects of ability remain small but persistent. In comparing men and women, substantial differences are found in career trajectories and in life course changes in occupational returns to schooling.

Occupational Stratification across the Life Course: Evidence from the Wisconsin Longitudinal Study

Sociologists frequently study changes across cohorts in the consequences of family background, gender, education, and cognitive ability for occupational outcomes. This study focuses, however, on how the consequences of these variables change within the course of individuals' lives. To appropriately estimate changes across the life course in the determinants of occupational standing, corrections are made for measurement errors in variables, and data on siblings are used to account for all aspects (measured and unmeasured) of family background. The analyses use data from the Wisconsin Longitudinal Study, which provides multiple measures of siblings'occupational standing at four points in their lives. Models of sibling resemblance show that the effects of family background on occupational standing operate entirely through their effects on education and cognitive ability. The effects of education decline across the life course, while the effects of ability remain small but persistent. In comparing men and women, substantial differences are found in career trajectories and in life course changes in occupational returns to schooling.

A Summary of Tritium In-Bed Accountability for 1500 Liter LaNi4.25Al0.75 Storage Beds

ABSTRACTIn-bed accountability (IBA), a steady-state, flowing gas calorimetric method, has been implemented for production measurement of tritium inventories in metal hydride storage beds utilizing a LaNi4.25Al0.25 metal hydride alloy. Six-point calibration curves have been completed for six, nominal 390 gram, and two nominal 1310 gram tritium metal hydride storage beds. The equations used to calculate inventory errors are derived and presented in the Appendix. Beds with the same amount of insulation gave similar IBA calibration curves and bed temperature versus tritium inventory results. Tritium IBA inventory measurement errors varied slightly with bed inventory and maximum values at the 95% confidence level ranged from 4 to 9 grams for the 390 gram beds (1.1 to 2.6%) and from 8 to 13 grams for the 1310 gram beds (0.7 to 1.2%). Comparison of other methods for determining inventories on the same beds (hydride pressure, hydride bed temperature, and hydride bed temperature rise above the glove box temperature) showed the IBA method gave the highest accuracy tritium measurements. These other inventory methods also showed greater variability in measurement error over the range of tritium inventories, van’t Hoff plots of hydride bed pressure under steady-state IBA conditions revealed a reduction in hydride pressure after several months of tritium service compared to other beds without tritium exposure.

Consistent fundamental matrix estimation in a quadratic measurement error model arising in motion analysis

Consistent estimators of the rank-deficient fundamental matrix yielding information on the relative orientation of two images in two-view motion analysis are derived. The estimators are derived by minimizing a corrected contrast function in a quadratic measurement error model. In addition, a consistent estimator for the measurement error variance is obtained. Simulation results show the improved accuracy of the newly proposed estimator compared to the ordinary total least-squares estimator.

A Note on the Estimation of Linear Regression Models with Heteroskedastic Measurement Errors

I consider the estimation of linear regression models when the independent variables are measured with errors whose variances differ across observations, a situation that arises, for example, when the explanatory variables in a regression model are estimates of population parameters based on samples of varying sizes. Replacing the error variance that is assumed common to all observations in the standard errors-in-variables estimator by the mean measurement error variance yields a consistent estimator in the case of measurement error heteroskedasticity. However, another estimator, which I call the Heteroskedastic Errors in Variables Estimator (HEIV), is, under standard assumptions, asymptotically more efficient. Simulations show that the efficiency gains are likely to appreciable in practice. In addition, the HEIV estimator, which is equal to the ordinary least squares regression of the dependent variable on the best linear predictor of the true independent variables, is simple to compute with standard regression software.

A Procedure of Reconstruction of the Climatic Seasonal Circulation in the Black Sea Based on the Assimilation of Hydrological Data in the Model

We propose a procedure of reconstruction of the continuous (in time) climatic annual behavior of circulation in the Black Sea based on the successive assimilation of the climatic distributions of temperature and salinity in the complete nonlinear model. We use monthly average arrays interpolated for each day of a year by expanding in harmonic functions of time. Various procedures aimed at the assimilation of data are studied by taking into account the variance of measurement errors. Our main attention is given to the analysis of qualitative and quantitative characteristics of vertical motions in the sea depending on the quality of the data and parameters of the model. The main version of calculations is illustrated by the maps of annual variability of the fields of sea level, horizontal currents, and vertical velocity.