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 On The Errors-In-Variables Model With Singular Dispersion Matrices

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
B. Schaffrin ◽  
K. Snow ◽  
F. Neitzel
Keyword(s):  
Measurement Error ◽  
Similarity Transformation ◽  
Total Least Squares ◽  
Data Matrix ◽  
Errors In Variables ◽  
Minimum Eigenvalue ◽  
Rank Condition ◽  
Data Vector ◽  
Special Case ◽  
General Measurement

AbstractWhile the Errors-In-Variables (EIV) Model has been treated as a special case of the nonlinear Gauss- Helmert Model (GHM) for more than a century, it was only in 1980 that Golub and Van Loan showed how the Total Least-Squares (TLS) solution can be obtained from a certain minimum eigenvalue problem, assuming a particular relationship between the diagonal dispersion matrices for the observations involved in both the data vector and the data matrix. More general, but always nonsingular, dispersion matrices to generate the “properly weighted” TLS solution were only recently introduced by Schaffrin and Wieser, Fang, and Mahboub, among others. Here, the case of singular dispersion matrices is investigated, and algorithms are presented under a rank condition that indicates the existence of a unique TLS solution, thereby adding a new method to the existing literature on TLS adjustment. In contrast to more general “measurement error models,” the restriction to the EIV-Model still allows the derivation of (nonlinear) closed formulas for the weighted TLS solution. The practicality will be evidenced by an example from geodetic science, namely the over-determined similarity transformation between different coordinate estimates for a set of identical points.

scholarly journals Validity of Absolute Intake and Nutrient Density of Protein, Potassium, and Sodium Assessed by Various Dietary Assessment Methods: An Exploratory Study

Nutrients ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 109
Author(s):  
Laura Trijsburg ◽  
Anouk Geelen ◽  
Paul J.M. Hulshof ◽  
Pieter van’t Veer ◽  
Hendriek C. Boshuizen ◽  
...  
Keyword(s):  
Total Energy ◽  
Measurement Errors ◽  
Sodium Intake ◽  
Dietary Assessment ◽  
Dietary Exposure ◽  
Assessment Methods ◽  
Doubly Labelled Water ◽  
Web Based ◽  
Dietary Assessment Methods ◽  
Nutrient Density

It is suggested that nutrient densities are less affected by measurement errors than absolute intake estimates of dietary exposure. We compared the validity of absolute intakes and densities of protein (kJ from protein/total energy (kJ)), potassium, and sodium (potassium or sodium (in mg)/total energy (kJ)) assessed by different dietary assessment methods. For 69 Dutch subjects, two duplicate portions (DPs), five to fifteen 24-h dietary recalls (24 hRs, telephone-based and web-based) and two food frequency questionnaires (FFQs) were collected and compared to duplicate urinary biomarkers and one or two doubly labelled water measurements. Multivariate measurement error models were used to estimate validity coefficients (VCs) and attenuation factors (AFs). This research showed that group bias diminished for protein and sodium densities assessed by all methods as compared to the respective absolute intakes, but not for those of potassium. However, the VCs and AFs for the nutrient densities did not improve compared to absolute intakes for all four methods; except for the AF of sodium density (0.71) or the FFQ which was better than that of the absolute sodium intake (0.51). Thus, using nutrient densities rather than absolute intakes does not necessarily improve the performance of the DP, FFQ, or 24 hR.

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 On the smallest singular value of symmetric random matrices

2021 ◽  
pp. 1-22
Author(s):  
Vishesh Jain ◽  
Ashwin Sah ◽  
Mehtaab Sawhney
Keyword(s):  
Random Matrices ◽  
Symmetric Matrix ◽  
Geometric Approach ◽  
Random Variable ◽  
Symmetric Matrices ◽  
Common Denominator ◽  
Geometric Framework ◽  
Small Constant ◽  
Special Case ◽  
Smallest Singular Value

Abstract We show that for an $n\times n$ random symmetric matrix $A_n$ , whose entries on and above the diagonal are independent copies of a sub-Gaussian random variable $\xi$ with mean 0 and variance 1, \begin{equation*}\mathbb{P}[s_n(A_n) \le \epsilon/\sqrt{n}] \le O_{\xi}(\epsilon^{1/8} + \exp(\!-\Omega_{\xi}(n^{1/2}))) \quad \text{for all } \epsilon \ge 0.\end{equation*} This improves a result of Vershynin, who obtained such a bound with $n^{1/2}$ replaced by $n^{c}$ for a small constant c, and $1/8$ replaced by $(1/8) - \eta$ (with implicit constants also depending on $\eta > 0$ ). Furthermore, when $\xi$ is a Rademacher random variable, we prove that \begin{equation*}\mathbb{P}[s_n(A_n) \le \epsilon/\sqrt{n}] \le O(\epsilon^{1/8} + \exp(\!-\Omega((\!\log{n})^{1/4}n^{1/2}))) \quad \text{for all } \epsilon \ge 0.\end{equation*} The special case $\epsilon = 0$ improves a recent result of Campos, Mattos, Morris, and Morrison, which showed that $\mathbb{P}[s_n(A_n) = 0] \le O(\exp(\!-\Omega(n^{1/2}))).$ Notably, in a departure from the previous two best bounds on the probability of singularity of symmetric matrices, which had relied on somewhat specialized and involved combinatorial techniques, our methods fall squarely within the broad geometric framework pioneered by Rudelson and Vershynin, and suggest the possibility of a principled geometric approach to the study of the singular spectrum of symmetric random matrices. The main innovations in our work are new notions of arithmetic structure – the Median Regularized Least Common Denominator (MRLCD) and the Median Threshold, which are natural refinements of the Regularized Least Common Denominator (RLCD)introduced by Vershynin, and should be more generally useful in contexts where one needs to combine anticoncentration information of different parts of a vector.

scholarly journals Biomarkers in nutritional epidemiology

2002 ◽  
Vol 5 (6a) ◽  
pp. 821-827 ◽  
Author(s):  
Sheila A Bingham
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Disease Risk ◽  
Dietary Assessment ◽  
Nutritional Epidemiology ◽  
Significant Development ◽  
Gene Environment ◽  
Human Volunteers ◽  
Individual Disease ◽  
Scientific Hypotheses

AbstractObjective:To illustrate biomarkers of diet that can be used to validate estimates of dietary intake in the study of gene–environment interactions in complex diseases.Design:Prospective cohort studies, studies of biomarkers where diet is carefully controlled.Setting:Free–living individuals, volunteers in metabolic suites.Subjects:Male and female human volunteers.Results:Recent studies using biomarkers have demonstrated substantial differences in the extent of measurement error from those derived by comparison with other methods of dietary assessment. The interaction between nutritional and genetic factors has so far largely gone uninvestigated, but can be studied in epidemiological trials that include collections of biological material. Large sample sizes are required to study interactions, and these are made larger in the presence of measurement errors.Conclusions:Diet is of key importance in affecting the risk of most chronic diseases in man. Nutritional epidemiology provides the only direct approach to the quantification of risks. The introduction of biomarkers to calibrate the measurement error in dietary reports, and as additional measures of exposure, is a significant development in the effort to improve estimates of the magnitude of the contribution of diet in affecting individual disease risk within populations. The extent of measurement error has important implications for correction for regression dilution and for sample size. The collection of biological samples to improve and validate estimates of exposure, enhance the pursuit of scientific hypotheses, and enable gene–nutrient interactions to be studied, should become the routine in nutritional epidemiology.

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 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.

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

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.

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