Calibration of Differently Measured Components of a Sum

• Activity Number: 491
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: International Indian Statistical Association
• Author(s): Kaushik Jana* and Debasis Sengupta and Kalyan Rudra
• Companies: Indian Statistical Institute and Indian Statistical Institute and West Bengal
• Keywords: Bifurcation ; Dependence measure ; Independence ; Multiplicative distortion ; Nonparametric estimation

Abstract

We consider an estimation problem, where two additive components of an aggregate quantity, the aggregate being independent of the proportion between the components, are measured with different degrees of fixed and multiplicative distortion. The goal is to estimate the ratio of the distortion factors, so that the measurements of the two components can be brought to a common scale. This problem is different from the problem usually referred to as `calibration' in the statistical literature, as there is no underlying deterministic function that relates the two measurements in an approximate sense. The present problem arises, for example, when the flows through different channels of a river controlling structure are measured by empirical formulae based on channel dimensions. We provide a class of distribution free and consistent estimators of the desired ratio, by exploiting the independence of the aggregate and the proportion of the two measured components. We perform Monte Carlo simulations of two specific estimators and compare their mean squared errors to the Cramer-Rao lower bound for the variance in the case of some choices of the underlying distributions. Finally, we use the pro