Chiang Mai Journal of Science

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This paper presents prediction intervals for difference between two future sample means when the distributions are non-normal distributed with missing data. We imputed values for the missing data in a random sample {X_1,i;i=1,...,m₁} and {X_2,i;i=1,...,m₂} based on the random hot deck imputation method. The prediction intervals considered are nonadaptive prediction interval (PI) and the adaptive interval that incorporates a preliminary test of symmetry for the underlying distributions (PI_adps). If the preliminary test fails to reject symmetry for both distributions, the adaptive prediction interval uses the non-adaptive prediction interval; otherwise, it uses the non-adaptive prediction interval to the log-transformed data, then the interval is transformed back. Simulation studies show that under imputation for item nonresponse, the adaptive prediction interval that incorporates the test of  symmetry contains the difference between two future sample means better than the non-adaptive prediction interval.

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