Abstract: This paper studies the proportional Bootstrap method on missing data, and
compares it with the usual Bootstrap method. Under the simple random sampling and
uniform response, using regression imputation and ratio imputation for missing data,
the consistency of the variance estimators obtained by proportional Bootstrap is proved.
Simulation results give a verification on our theoretical conclusions.

Key words: Bootstrap, Consistency, Proportional Bootstrap, Ratio imputation, Re- gression imputation, Variance estimation.