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CPS2224 Habshah Midi et al.
4. Discussion and Conclusion
Primarily, the least square fixed effect regression provides the best linear
unbiased estimator (BLUE) under the assumptions of normally distributed,
independent and identically distributed errors. However, the presence of
simultaneous distortions towards normality and homoscedasticity of the error
terms often lead to wrong statistical analysis and conclusions of the method.
Thus, this study proposes heteroskedasticity and outlier-robust estimator and
its algorithm are proposed to dampen the effects of heteroskedasticity and
also high leverage values. In the first step of Two Step HO (TSHO) a procedure
is taken to reduce the influence of heteroskedasticity by placing appropriate
weights to the residuals. Consequently, the second step guards against the
fatal effects of high leverage values by introducing robust weights. The TSHO
uses residuals by RWGM(RDF) to warrant only true high leverage values to be
given low robust weights. In this way, potential outliers or high leverage values
are investigated and dealt with appropriately. The simulation and numerical
studies reveal the reliability of the respective TSHO algorithm. Fixed effect
data are completely distorted in the presence of the highly contagious block
HLPs. The success of TSHO regression in providing efficient estimates under
the condition of heteroskedastic and non-normal errors show that when
weights can be estimated appropriately, weighted least squares becomes a
superior least squares analysis. (Carroll and Ruppert, 1982; Ryan, 1997).

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