Statistical Inference for Inverse Regression Prediction with Applications to Tooth Dosimetry

• Activity Number: 232
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Eugene Demidenko*+
• Companies: Dartmouth Medical School
• Keywords: inverse regression ; statistical inference ; prediction

Abstract

Many statistical problems lead to inverse regression prediction: if a and b are the least squares estimates in a simple linear regression the predictor is estimated as (y-a)/b. Under standard normal assumption, the distribution of this inverse regression predictor follows the Cauchy distribution and as such does not have finite mean and variance. Thus, the standard statistical inference does not apply. We develop relevant approximate and exact confidence intervals and hypothesis testing for inverse regression. A new statistical figure of merit for inverse regression is introduced, the Standard Error of Inverse Prediction (SEIP), that can be viewed as the inverse regression goodness-of-fit measure. SEIP can be used to characterize the quality of inverse prediction and facilitate the optimal choice of the regression model. These methods and the advanced statistical inference are applied to the Electron Paramagnetic Resonance (EPR) tooth dosimetry for the rapid reconstruction of radiation dose in the case of nuclear terrorism.