Page 278 - Contributed Paper Session (CPS) - Volume 4

CPS2224 Habshah Midi et al.
Step Heteroskedasticity-Outlier (TSHO) robust estimator which consists of two
important steps to guard against the vulnerability of outliers and also
heteroskedastic errors. Crucial steps are taken to dampen the heteroskedastic
condition and lower weights are assigned to outlying observations to produce
more reliable fixed effect estimates. The second objective is to investigate the
performance the newly proposed method and the performance behaviour of
existing methods such as Robust Within Group Generalized M or RWGM
(Bramati and Croux, 2007) and FGLS under the violations of the least square
assumptions of non-normal and heteroskedastic errors. Empirical evidence
on the performance of the newly proposed method, Two Step HO (TSHO) will
be provided by comparing its performance with the existing methods under
different data centering procedures.
The paper proceeds as follows. The next section presents the proposed
TSHO based on weighted least squares. The method’s first step consists of a
procedure to correct heteroskedasticity. On the other hand, different weights
are introduced in the second step to dampen the effects of outlying values.
Section 3 provides the results of TSHO when applied to real data with
conditions of heteroskedasticity and non-normality. Comparisons are made
with other methods such as RWGM and also the conventional FGLS.
Conclusion of the paper is presented in the Section 4.

2. Methodology
The newly proposed Two Step Heteroskedasticity-Outlier (TSHO) robust
estimation involves two vital steps in which two different types of weights are
determined to protect against the fatal effects of heteroskedasticity and
outlying values. The first weight is evaluated by using F values (Djauhari, 2010)
determined by the Robust Diagnostic-F from Midi and Abu Bakar (2015). On
the other hand, the second weight is determined by log transformation of the
residuals to dampen heteroskedasticity. The following steps describe the
algorithm of TSHO and the derivation of the new weights.
Step 1: Transform panel data by robust MM-centering (Abu Bakar and Midi,
2015)
Step 2: Determine the first weights, by using the newly proposed Robust
Diagnostic-F or RDF (Midi and Abu Bakar, 2015). Tukey’s Biweight function is
selected to determine ; meant to down weigh any observation with large
residual. The tuning function of Biweight function is chosen to be 4.685 to
provide a balance between efficiency and robustness (Wagenvoort and
Waldmann, 2002). The diagonal elements of the second weighting matrix W
O
is rewritten as
 cutoff 
W = min 1, RDF
O  
 F 

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