Statistica Sinica 9(1999), 247-261

AN ASYMPTOTICALLY HONEST PREDICTION SET

FOR THE MULTIVARIATE REGRESSION MODEL

WHEN THE RESPONSE IS MEASURED WITH ERROR

Steve Y. H. Huang and Longcheen Huwang

National Tsing Hua University

Abstract: This paper constructs an asymptotically honest prediction set for the response variable, measured with error, in the multivariate regression model. By asymptotic honesty we mean that the limit inferior of the infimum coverage probability over the parameter space converges to the nominal level as the sample size goes to ∞. In the univariate case a desirable property of the length of this asymptotically honest prediction interval is obtained. A small simulation study shows that the coverage probability of this prediction set is close to the nominal level in the finite sample as well. Finally, we show that in errors-in-variables models, calibration and prediction problems can be solved by treating the models as special cases of the aforementioned model when the errors and the calibrated variables are assumed to be normally distributed.

Key words and phrases: Coverage probability, prediction set, regression model.