On the identifiability of errors-in-variables models with white measurement errors

Automatica ◽  
2011 ◽  
Vol 47 (3) ◽  
pp. 545-551 ◽  
Author(s):  
Giulio Bottegal ◽  
Giorgio Picci ◽  
Stefano Pinzoni
Keyword(s):  
Measurement Errors ◽  
Errors In Variables

Nonlinear Models of Measurement Errors

2011 ◽  
Vol 49 (4) ◽  
pp. 901-937 ◽  
Author(s):  
Xiaohong Chen ◽  
Han Hong ◽  
Denis Nekipelov
Keyword(s):  
Economic Analysis ◽  
Instrumental Variable ◽  
Measurement Errors ◽  
Nonlinear Models ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Discrete Variables ◽  
Errors In Variables ◽  
Economic Data ◽  
Research Papers

Measurement errors in economic data are pervasive and nontrivial in size. The presence of measurement errors causes biased and inconsistent parameter estimates and leads to erroneous conclusions to various degrees in economic analysis. While linear errors-in-variables models are usually handled with well-known instrumental variable methods, this article provides an overview of recent research papers that derive estimation methods that provide consistent estimates for nonlinear models with measurement errors. We review models with both classical and nonclassical measurement errors, and with misclassification of discrete variables. For each of the methods surveyed, we describe the key ideas for identification and estimation, and discuss its application whenever it is currently available. (JEL C20, C26, C50)

scholarly journals Self-Consistent Density Estimation in the Presence of Errors-in-Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Junhua Zhang ◽  
Yuping Hu ◽  
Sanying Feng
Keyword(s):  
Measurement Errors ◽  
Kernel Method ◽  
Error Distribution ◽  
The Self ◽  
Errors In Variables ◽  
Mean Integrated Square Error ◽  
Self Consistent ◽  
The Common ◽  
The Mean ◽  
Consistency Properties

This paper considers the estimation of the common probability density of independent and identically distributed variables observed with additive measurement errors. The self-consistent estimator of the density function is constructed when the error distribution is known, and a modification of the self-consistent estimation is proposed when the error distribution is unknown. The consistency properties of the proposed estimators and the upper bounds of the mean square error and mean integrated square error are investigated under some suitable conditions. Simulation studies are carried out to assess the performance of our proposed method and compare with the usual deconvolution kernel method. Two real datasets are analyzed for further illustration.

scholarly journals Changepoint in Error-Prone Relations

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 89
Author(s):  
Michal Pešta
Keyword(s):  
Measurement Errors ◽  
Dietary Assessment ◽  
Data Matrix ◽  
Nuisance Parameters ◽  
Errors In Variables ◽  
Weak Invariance Principle ◽  
Testing Procedures ◽  
Clinical Measurements ◽  
Special Case ◽  
Smallest Singular Value

Linear relations, containing measurement errors in input and output data, are considered. Parameters of these so-called errors-in-variables models can change at some unknown moment. The aim is to test whether such an unknown change has occurred or not. For instance, detecting a change in trend for a randomly spaced time series is a special case of the investigated framework. The designed changepoint tests are shown to be consistent and involve neither nuisance parameters nor tuning constants, which makes the testing procedures effortlessly applicable. A changepoint estimator is also introduced and its consistency is proved. A boundary issue is avoided, meaning that the changepoint can be detected when being close to the extremities of the observation regime. As a theoretical basis for the developed methods, a weak invariance principle for the smallest singular value of the data matrix is provided, assuming weakly dependent and non-stationary errors. The results are presented in a simulation study, which demonstrates computational efficiency of the techniques. The completely data-driven tests are illustrated through problems coming from calibration and insurance; however, the methodology can be applied to other areas such as clinical measurements, dietary assessment, computational psychometrics, or environmental toxicology as manifested in the paper.

scholarly journals Beta regression model nonlinear in the parameters with additive measurement errors in variables

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254103
Author(s):  
Daniele de Brito Trindade ◽  
Patrícia Leone Espinheira ◽  
Klaus Leite Pinto Vasconcellos ◽  
Jalmar Manuel Farfán Carrasco ◽  
Maria do Carmo Soares de Lima
Keyword(s):  
Measurement Errors ◽  
Regression Models ◽  
Oil Refinery ◽  
Model Parameters ◽  
Beta Regression ◽  
Real Problem ◽  
Errors In Variables ◽  
Likelihood Approximation ◽  
Pseudo Likelihood ◽  
Interval Estimators

We propose in this paper a general class of nonlinear beta regression models with measurement errors. The motivation for proposing this model arose from a real problem we shall discuss here. The application concerns a usual oil refinery process where the main covariate is the concentration of a typically measured in error reagent and the response is a catalyst’s percentage of crystallinity involved in the process. Such data have been modeled by nonlinear beta and simplex regression models. Here we propose a nonlinear beta model with the possibility of the chemical reagent concentration being measured with error. The model parameters are estimated by different methods. We perform Monte Carlo simulations aiming to evaluate the performance of point and interval estimators of the model parameters. Both results of simulations and the application favors the method of estimation by maximum pseudo-likelihood approximation.

scholarly journals Asymptotic normality of a simple linear EV regression model with martingale difference errors

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1817-1825
Author(s):  
Guo-Liang Fan ◽  
Tian-Heng Chen
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Error Variance ◽  
Martingale Difference ◽  
Errors In Variables ◽  
Ev Regression Model ◽  
Biased Estimators ◽  
Better Than

This paper considers the estimation of a linear EV (errors-in-variables) regression model under martingale difference errors. The usual least squares estimations lead to biased estimators of the unknown parametric when measurement errors are ignored. By correcting the attenuation we propose a modified least squares estimator for a parametric component and construct the estimators of another parameter component and error variance. The asymptotic normalities are also obtained for these estimators. The simulation study indicates that the modified least squares method performs better than the usual least squares method.

scholarly journals Comparing estimation methods of non-stationary errors-in-variables models

2019 ◽  
Vol 3 (1) ◽  
pp. 73-101 ◽  
Author(s):  
Naoto Kunitomo ◽  
Naoki Awaya ◽  
Daisuke Kurisu
Keyword(s):  
Maximum Likelihood ◽  
Measurement Errors ◽  
Likelihood Function ◽  
Asymptotic Properties ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Errors In Variables ◽  
Economic Time Series ◽  
Finite Sample ◽  
Ml Estimation

AbstractWe investigate the estimation methods of the multivariate non-stationary errors-in-variables models when there are non-stationary trend components and the measurement errors or noise components. We compare the maximum likelihood (ML) estimation and the separating information maximum likelihood (SIML) estimation. The latter was proposed by Kunitomo and Sato (Trend, seasonality and economic time series: the nonstationary errors-in-variables models. MIMS-RBP-SDS-3, MIMS, Meiji University. http://www.mims.meiji.ac.jp/, 2017) and Kunitomo et al. (Separating information maximum likelihood method for high-frequency financial data. Springer, Berlin, 2018). We have found that the Gaussian likelihood function can have non-concave shape in some cases and the ML method does work only when the Gaussianity of non-stationary and stationary components holds with some restrictions such as the signal–noise variance ratio in the parameter space. The SIML estimation has the asymptotic robust properties in more general situations. We explore the finite sample and asymptotic properties of the ML and SIML methods for the non-stationary errors-in variables models.

scholarly journals Strong consistency rates of estimators in semi-parametric errors-in-variables model with missing responses

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6073-6089
Author(s):  
Jingjing Zhang ◽  
Linran Zhang
Keyword(s):  
Measurement Errors ◽  
Strong Consistency ◽  
Missing At Random ◽  
Slope Parameter ◽  
Errors In Variables ◽  
Missing Responses ◽  
Error In Variables ◽  
Response Variables

In this article, we focus on the semi-parametric error-in-variables model with missing responses: yi = ?i? + g(ti)+ ?i,xi = ?i + ?i, where yi are the response variables missing at random, (?i,ti) are design points, ?i are the potential variables observed with measurement errors ?i, the unknown slope parameter ? and nonparametric component g(?) need to be estimate. Here we choose three different approaches to estimate ? and g(?). Under appropriate conditions, we study the strong consistency rates for the proposed estimators. In general, we concluded that the strong consistency rates for all estimators can achieve o(n-1/4).

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