# Model Diagnostics in the presence of measurement error

 dc.contributor.author Prof. Hira Lal Koul dc.date.accessioned 2015-03-09T05:28:22Z dc.date.available 2015-03-09T05:28:22Z dc.date.issued 2015-03-09 dc.identifier.uri http://dyuthi.cusat.ac.in/purl/4918 dc.description.abstract The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. en_US As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v. dc.description.sponsorship Cochin University of science & Technology and Kerala State Higher Education Council en_US dc.language.iso en en_US dc.relation.ispartofseries Michigan State University, USA; dc.subject Model Diagnostics in the presence of measurement error en_US dc.subject Model Diagnostics via Khmaladze's Martingale Transform en_US dc.subject Model diagnostics in the presence of incomplete observations en_US dc.title Model Diagnostics in the presence of measurement error en_US dc.type Technical Report en_US
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