ON THE UNIFORM CONVERGENCE OF DECONVOLUTION ESTIMATORS FROM REPEATED MEASUREMENTS

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

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Bayesian Estimation Analysis of Bernoulli Measurement Error Model for Longitudinal Data

International Journal of Applied Physics and Mathematics ◽

10.17706/ijapm.2020.10.4.160-166 ◽

2020 ◽

Vol 10 (4) ◽

pp. 160-166

Author(s):

Dewang Li ◽

◽

Meilan Qiu ◽

Zhongyi Ke

Keyword(s):

Measurement Error ◽

Longitudinal Data ◽

Bayesian Statistics ◽

Measurement Errors ◽

Bayesian Method ◽

Error Model ◽

Simulation Studies ◽

Unknown Parameters ◽

Measurement Error Model ◽

Mh Algorithm

The Bayesian method is used to study the inference of the semi-parametric measurement error model (MEs) with longitudinal data. A semi-parametric Bayesian method combined with fracture prior and Gibbs sampling combined with Metropolis-Hastings (MH) algorithm is applied and applied to the simulation observation from the posterior distribution, and the combined Bayesian statistics of unknown parameters and measurement errors are obtained. We obtained Bayesian estimates of the parameters and covariates of the measurement error model. Under three different priori assumptions, four simulation studies illustrate the effectiveness and utility of the proposed method.

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Bayesian adjustment for measurement error in an offset variable in a Poisson regression model

Statistical Modelling ◽

10.1177/1471082x211008011 ◽

2021 ◽

pp. 1471082X2110080

Author(s):

Kangjie Zhang ◽

Juxin Liu ◽

Yang Liu ◽

Peng Zhang ◽

Raymond J. Carroll

Keyword(s):

Measurement Error ◽

Random Effects ◽

Spatial Data ◽

Poisson Regression ◽

Measurement Errors ◽

Error Model ◽

County Level ◽

Measurement Error Model ◽

The Usa ◽

Car Crashes

Fatal car crashes are the leading cause of death among teenagers in the USA. The Graduated Driver Licensing (GDL) programme is one effective policy for reducing the number of teen fatal car crashes. Our study focuses on the number of fatal car crashes in Michigan during 1990–2004 excluding 1997, when the GDL started. We use Poisson regression with spatially dependent random effects to model the county level teen car crash counts. We develop a measurement error model to account for the fact that the total teenage population in the county level is used as a proxy for the teenage driver population. To the best of our knowledge, there is no existing literature that considers adjustment for measurement error in an offset variable. Furthermore, limited work has addressed the measurement errors in the context of spatial data. In our modelling, a Berkson measurement error model with spatial random effects is applied to adjust for the error-prone offset variable in a Bayesian paradigm. The Bayesian Markov chain Monte Carlo (MCMC) sampling is implemented in rstan. To assess the consequence of adjusting for measurement error, we compared two models with and without adjustment for measurement error. We found the effect of a time indicator becomes less significant with the measurement-error adjustment. It leads to our conclusion that the reduced number of teen drivers can help explain, to some extent, the effectiveness of GDL.

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Measurement error model for the Norwegian common minke whale (Balaenoptera acutorostrata acutorostrata) surveys 2008-2013

J. Cetacean Res. Manage. ◽

10.47536/jcrm.v22i1.158 ◽

2021 ◽

Vol 22 (1) ◽

pp. 01-16

Author(s):

Hiroko Solvang

Keyword(s):

Measurement Error ◽

Measurement Errors ◽

Radial Distance ◽

Error Model ◽

Line Transect ◽

Balaenoptera Acutorostrata ◽

Measurement Error Model ◽

Abundance Estimates ◽

Discrete Measurement ◽

Measurement Error Correction

A discrete measurement error model for radial distance and angle to detected objects in line transect surveys is considered. This approach directly quantifies the effect of measurement error on the estimated effective strip half-width. We apply the method to experimental data collected over the period 2008-2013 in North Atlantic both under the assumption of multiplicative and additive measurement errors. Our results indicate that the abundance estimates considering the measurement error are consistently larger than the abundance estimates without any measurement error correction.

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