Confidence Intervals in Regression That Utilize Uncertain Prior Information
Paul Kabaila
Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria, Australia

Kabaila and Giri (2009) JSPI, consider a linear regression model with independent and identically normally distributed errors. The parameter of interest theta is a specified linear combination of the regression parameters. They suppose that there is uncertain prior information about a different specified linear combination of these parameters. This prior information may arise from previous experience with similar data sets and/or expert opinion and scientific background. They describe a new frequentist 1-alpha confidence interval for theta that utilizes this uncertain prior information. This confidence interval has coverage probability 1-alpha throughout the parameter space. They define the scaled expected length of this confidence interval to be its expected length divided by the expected length of the usual 1-alpha confidence interval for theta. The new confidence interval utilizes this uncertain prior information in the sense that the following three conditions hold. The first condition is that the scaled expected length is significantly less than 1 when the prior information is correct. The second condition is that the maximum (over the parameter space) of the scaled expected length is not too much larger than 1. The third condition is that the confidence interval reverts to the usual 1-alpha confidence interval when the data happen to strongly contradict the prior information. In this talk, I will describe some extensions of this work of Kabaila and Giri (2009) JSPI.

Keywords: Frequentist confidence interval; Prior information; Linear regression

Biography: Dr. Paul Kabaila holds a Reader in Statistics position in the Department of Mathematics and Statistics at La Trobe University in Melbourne, Australia. He has 75 publications in international refereed journals and is an elected member of the International Statistical Institute. His research interests include: (a) frequentist confidence intervals and prediction intervals that utilize uncertain prior information, (b) the effect of preliminary model selection on confidence intervals and prediction intervals, (c) exact confidence intervals from count data and (d) time series prediction intervals that account for parameter estimation errors.