Use of prior information in the consistent estimation of regression coefficients in measurement error models

  • Authors:

  • Shalabh;Gaurav Garg;Neeraj Misra

  • Affiliations:

  • Department of Mathematics & Statistics, Indian Institute of Technology Kanpur, Kanpur - 208 016, India;Department of Mathematics, Jaypee University of Information Technology, Waknaghat - 173 215, Solan, H.P., India;Department of Mathematics & Statistics, Indian Institute of Technology Kanpur, Kanpur - 208 016, India

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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Abstract

A multivariate ultrastructural measurement error model is considered and it is assumed that some prior information is available in the form of exact linear restrictions on regression coefficients. Using the prior information along with the additional knowledge of covariance matrix of measurement errors associated with explanatory vector and reliability matrix, we have proposed three methodologies to construct the consistent estimators which also satisfy the given linear restrictions. Asymptotic distribution of these estimators is derived when measurement errors and random error component are not necessarily normally distributed. Dominance conditions for the superiority of one estimator over the other under the criterion of Lowner ordering are obtained for each case of the additional information. Some conditions are also proposed under which the use of a particular type of information will give a more efficient estimator.