Application of Uniform Measurement Error Distribution

2016 ◽  
Author(s):  
Alan Ghazarians ◽  
Subrata Sanyal ◽  
Dennis H. Jackson
Keyword(s):  
Measurement Error ◽  
Error Distribution ◽  
Uniform Measurement

Some sources of error and possible bias in Danscan ultrasonic measurements of cattle

1983 ◽  
Vol 37 (1) ◽  
pp. 67-71
Author(s):  
J. P. Gibson ◽  
J. C. Alliston
Keyword(s):  
Measurement Error ◽  
Mean Value ◽  
Time Of Day ◽  
Error Distribution ◽  
The Body ◽  
Residual Error ◽  
Ultrasonic Measurements ◽  
The Mean ◽  
Ultrasonic Images ◽  
Account Variation

ABSTRACTPhotographs of ultrasonic images of 10 animals were taken. Two replicate photographs were taken at each of four body positions (10th rib, 13th rib, 3rd lumbar and hindquarter) on both sides of the body in the morning and the afternoon of the day of scanning. Several measurements were taken on each photograph by an experienced interpreter. Replicate photographs failed to account for all possible sources of measurement error. Since neither time of day nor side of the body affected the mean value, taking observations at different times of the day or on both sides of the body could permit most sources of measurement error to be taken into account. Variation due to errors of measurement and differences among animals are presented. The residual error distribution contained several extreme outliers.It was concluded that a better understanding of all the sources of bias and error will be needed if ultrasonic measurements are to be more widely used.

scholarly journals Estimation in linear errors-in-variables models with unknown error distribution

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 841-856
Author(s):  
Linh H Nghiem ◽  
Michael C Byrd ◽  
Cornelis J Potgieter
Keyword(s):  
Parameter Estimation ◽  
Measurement Error ◽  
Method Of Moments ◽  
Phase Function ◽  
Generalized Method Of Moments ◽  
Error Distribution ◽  
Outcome Variable ◽  
Model Parameters ◽  
Errors In Variables ◽  
Error Distributions

Summary Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based on the phase function, a normalized version of the characteristic function, is considered. This approach requires the model covariates to have asymmetric distributions, while the error distributions are symmetric. Parameters are estimated by minimizing a distance function between the empirical phase functions of the noisy covariates and the outcome variable. No knowledge of the measurement error distribution is needed to calculate this estimator. Both asymptotic and finite-sample properties of the estimator are studied. The connection between the phase function approach and method of moments is also discussed. The estimation of standard errors is considered and a modified bootstrap algorithm for fast computation is proposed. The newly proposed estimator is competitive with the generalized method of moments, despite making fewer model assumptions about the moment structure of the measurement error. Finally, the proposed method is applied to a real dataset containing measurements of air pollution levels.

Measurement error models with a general class of error distribution

Statistics ◽  
2009 ◽  
Vol 44 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Alexandre Galvão Patriota ◽  
Heleno Bolfarine
Keyword(s):  
Measurement Error ◽  
General Class ◽  
Error Distribution ◽  
Error Models ◽  
Measurement Error Models

Normal law of measurement error distribution

1962 ◽  
Vol 5 (4) ◽  
pp. 271-272
Author(s):  
G. S. Simkin
Keyword(s):  
Measurement Error ◽  
Error Distribution ◽  
Normal Law

INFLUENCE OF MEASUREMENT ERROR DISTRIBUTION THE ACCURACY RATES OF THE CONTROL

2020 ◽  
pp. 48-52
Author(s):  
S. B. Danilevich ◽  
V. V. Tretyak
Keyword(s):  
Measurement Error ◽  
Measurement Uncertainty ◽  
Uniform Distribution ◽  
Error Distribution ◽  
Reliability Indicators ◽  
The Monte Carlo Method ◽  
Accuracy Of Measurements ◽  
Accuracy Rates ◽  
Weakly Dependent

The influence of the type of distribution of measurement error and measurement uncertainty on the reliability of the multiparameter measurement testing is studied. Indicators of testing reliability include the probability of a control error of type 2 (P2), as well as the risk of the customer Rз and the risk of the manufacturer Rп. These control reliability indicators were calculated for different values of measurement uncertainty. The study was performed using the Monte Carlo method (imitation modelling). Three models of measurement error distribution were used: normal distribution, triangular (Simpson) distribution, uniform distribution. The results obtained allow us to establish the measurement uncertainty that provides the required risk of the customer (or another indicator of reliability). The following was established. For the symmetric law of error distribution, the highest estimates of the reliability indicators take place with a uniform distribution of the measurement error. The probability of P2 is weakly dependent on the number of controlled parameters and the type of distribution of the measurement error, but it significantly depends on the accuracy of measurements. The customer's risk depends significantly on both the number of controlled parameters and the accuracy of measurements during control.

scholarly journals The Construction Method of BeiDou Satellite Navigation Measurement Error System

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Jun Xie ◽  
Jian-jun Zhang ◽  
Gang Wang
Keyword(s):  
Measurement Error ◽  
Estimation Method ◽  
Satellite Navigation ◽  
Error Distribution ◽  
Distribution Model ◽  
Empirical Estimation ◽  
Satellite Navigation System ◽  
Error System ◽  
Error Index ◽  
The Relationship

Based on the measurement error of pseudorange in BeiDou satellite navigation system, this paper analyzes the measurement principle of the system. Aiming at the difficulties in the system measurement error index system, an overall construction method of measurement error system based on empirical estimation method and error distribution model is proposed. Based on the Analytic Hierarchy Process, the correlation analysis model of the measurement error index is constructed, the relationship between the indicators is analyzed, and the system measurement error index hierarchy is constructed. Based on the empirical estimation method and the error distribution model, the index values are decomposed and assigned based on the final service performance of the system, and a clear representation of the complex relationship of index matching is achieved. Finally, by analyzing the principle of the positioning function in the ground transportation control mode, taking the satellite clock error as an example, the model is decomposed layer by layer and the relevant indicator items are established. The relationship between index terms was studied, and the value of the indicators was quantified. Compared with the actual operating conditions of the current system, the correctness of the method was verified, which provided a basis for the demonstration of the index values of satellite navigation systems. Based on the empirical estimation method and error distribution model as a new type of calculation method, the index system established under a certain set of conditions is reasonable, and it can be applied to the error control adjustment in satellite navigation system engineering construction.

Benefits from Computerized Adaptive Testing as Seen in Simulation Studies

1999 ◽  
Vol 15 (2) ◽  
pp. 91-98 ◽  
Author(s):  
Lutz F. Hornke
Keyword(s):  
Measurement Error ◽  
Computerized Adaptive Testing ◽  
Test Procedure ◽  
Adaptive Testing ◽  
Parameter Estimates ◽  
Simulation Studies ◽  
Computerized Adaptive Test ◽  
Item Banks ◽  
Item Parameters ◽  
General Reliability

Summary: Item parameters for several hundreds of items were estimated based on empirical data from several thousands of subjects. The logistic one-parameter (1PL) and two-parameter (2PL) model estimates were evaluated. However, model fit showed that only a subset of items complied sufficiently, so that the remaining ones were assembled in well-fitting item banks. In several simulation studies 5000 simulated responses were generated in accordance with a computerized adaptive test procedure along with person parameters. A general reliability of .80 or a standard error of measurement of .44 was used as a stopping rule to end CAT testing. We also recorded how often each item was used by all simulees. Person-parameter estimates based on CAT correlated higher than .90 with true values simulated. For all 1PL fitting item banks most simulees used more than 20 items but less than 30 items to reach the pre-set level of measurement error. However, testing based on item banks that complied to the 2PL revealed that, on average, only 10 items were sufficient to end testing at the same measurement error level. Both clearly demonstrate the precision and economy of computerized adaptive testing. Empirical evaluations from everyday uses will show whether these trends will hold up in practice. If so, CAT will become possible and reasonable with some 150 well-calibrated 2PL items.

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