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Article
Estimating Smooth Distribution Function in the Presence of Heteroscedastic Measurement Errors
Computational Statistics and Data Analysis (2010)
  • Xiao-Feng Wang, Cleveland Clinic Lerner Research Institute
  • Zhaozhi Fan, Memorial University of Newfoundland
  • Bin Wang, University of South Alabama
Abstract
Measurement error occurs in many biomedical fields. The challenges arise when errors are heteroscedastic since we literally have only one observation for each error distribution. This paper concerns the estimation of smooth distribution function when data are contaminated with heteroscedastic errors. We study two types of methods to recover the unknown distribution function: a Fourier-type deconvolution method and a simulation extrapolation (SIMEX) method. The asymptotics of the two estimators are explored and the asymptotic pointwise confidence bands of the SIMEX estimator are obtained. The finite sample performances of the two estimators are evaluated through a simulation study. Finally, we illustrate the methods with medical rehabilitation data from a neuro-muscular electrical stimulation experiment.
Keywords
  • Smooth distribution function,
  • measurement errors,
  • deconvolution,
  • Fourier method;,
  • SIMEX,
  • heteroscedasticity
Disciplines
Publication Date
2010
Citation Information
Xiao-Feng Wang, Zhaozhi Fan and Bin Wang. "Estimating Smooth Distribution Function in the Presence of Heteroscedastic Measurement Errors" Computational Statistics and Data Analysis Vol. 54 Iss. 1 (2010)
Available at: http://works.bepress.com/wang/2/