Comparison of restricted maximum likelihood and bootstrap via minimum norm quadratic unbiased estimators for hierarchical linear models under \chi^2_1 assumptions

This study investigates whether the bootstrap via minimum norm quadratic es-
timation procedure offers improved accuracy in the estimation of the parameters
and their standard errors for a two-level hierarchical linear model when the observations follow a \chi^2_1 distribution. Through Monte Carlo simulations, the importance of this assumption for the accuracy of multilevel parameter estimates
and their standard errors is assessed using the accuracy index of absolute relative bias and by observing the coverage percentages of 95\% confidence intervals
constructed for both estimation procedures. Study results show that while both
the restricted maximum likelihood and the bootstrap via MINQUE estimates of
the fixed effects were accurate, the efficiencies of the estimates were affected by
the distribution of errors with both procedures producing less efficient estimators
under the  \chi^2_1 distribution, particularly for the variance-covariance component