Page 35 - Special Topic Session (STS) - Volume 1

STS346 Abu Sayed M. et al.
on the fitting of the model. When we use the ordinary least squares (OLS) or
the maximum likelihood (ML) method for fitting a regression line, the resulting
residuals are functions of leverages and true errors. Thus high leverage points
together with large errors (outliers) may pull the fitted line in a way that the
fitted residuals corresponding to those outliers might be too small and this
may cause masking (false negative) of outliers. For the same reason the
residuals corresponding to inliers may be too large and this may cause
swamping (false positive). Peña and Yohai (1995) pointed out that high
leverage cases are mainly responsible for masking and swamping of outliers
in linear regression. The unfortunate consequences of the presence of high
leverage points in linear regression have been studied by many authors. The
presence of a high leverage point could increase (often unduly) the value of.
Chatterjee and Hadi (1988) mentioned the existence of collinearity-influential
observations whose presence could induce or break the collinearity structure
among the explanatory variables. Kamruzzaman and Imon (2002) and Imon
and Khan (2003a) pointed out that high leverage points may be the prime
source of collinearity-influential observations. Imon (2009) pointed out that in
the presence of high leverage points the errors not only become
heteroscedastic, they might produce big outliers as well. This could make the
procedures for the detection of heteroscedasticity very complicated. That is
why the identification of high leverage points is essential before making any
kind of inference.
In this paper our main objective is to identify high leverage points in a
linear functional relationship model. Although some efforts have been done
on the identification of outliers and influential observations in LFRM e.g.
(Abdullah,1995; Vidal, 2007; and Wellman, 1991), but so far as we know, there
is no reported work in the identification of high leverage points in LFRM. Let
us consider a simple linear regression model
y     X   (1)
i
i
i
where y is the response, X is (supposed) explanatory variable assumed to

i
i
be constant and specific assumption made on . We feel that the assumption
i
of X being constant in model (1) may not appropriate in reality, instead we
i
introduce a linear functional relationship model.
Consider the following model y  Y   i , x  X   i ,
i
i
i
i
X
and Y     i , for i 1 2 , ,..., n (2)
i
where the two linearly related unobservable variables X and Y are considered
as the true part and the corresponding random variables x and y are observed
with random errors  and  i . The unobservable X and Y are fixed
i
(nonstochastic) and (2) is called a functional relation. So the main difference
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