<s>
In	O
statistics	O
,	O
errors-in-variables	B-Algorithm
models	I-Algorithm
or	O
measurement	B-Algorithm
error	I-Algorithm
models	I-Algorithm
are	O
regression	O
models	O
that	O
account	O
for	O
measurement	O
errors	O
in	O
the	O
independent	O
variables	O
.	O
</s>
<s>
For	O
simple	B-General_Concept
linear	I-General_Concept
regression	I-General_Concept
the	O
effect	O
is	O
an	O
underestimate	O
of	O
the	O
coefficient	O
,	O
known	O
as	O
the	O
attenuation	O
bias	O
.	O
</s>
<s>
Thus	O
the	O
‘	O
naïve’	O
least	B-General_Concept
squares	I-General_Concept
estimator	O
is	O
inconsistent	O
in	O
this	O
setting	O
.	O
</s>
<s>
It	O
can	O
be	O
argued	O
that	O
almost	O
all	O
existing	O
data	B-General_Concept
sets	I-General_Concept
contain	O
errors	O
of	O
different	O
nature	O
and	O
magnitude	O
,	O
so	O
that	O
attenuation	O
bias	O
is	O
extremely	O
frequent	O
(	O
although	O
in	O
multivariate	O
regression	O
the	O
direction	O
of	O
bias	O
is	O
ambiguous	O
)	O
.	O
</s>
<s>
Usually	O
measurement	B-Algorithm
error	I-Algorithm
models	I-Algorithm
are	O
described	O
using	O
the	O
latent	O
variables	O
approach	O
.	O
</s>
<s>
The	O
variables	O
,	O
,	O
are	O
all	O
observed	O
,	O
meaning	O
that	O
the	O
statistician	O
possesses	O
a	O
data	B-General_Concept
set	I-General_Concept
of	O
statistical	O
units	O
which	O
follow	O
the	O
data	O
generating	O
process	O
described	O
above	O
;	O
the	O
latent	O
variables	O
,	O
,	O
,	O
and	O
are	O
not	O
observed	O
however	O
.	O
</s>
<s>
This	O
specification	O
does	O
not	O
encompass	O
all	O
the	O
existing	O
errors-in-variables	B-Algorithm
models	I-Algorithm
.	O
</s>
<s>
For	O
example	O
in	O
some	O
of	O
them	O
function	O
may	O
be	O
non-parametric	B-General_Concept
or	O
semi-parametric	O
.	O
</s>
<s>
This	O
is	O
a	O
less	O
restrictive	O
assumption	O
than	O
the	O
classical	O
one	O
,	O
as	O
it	O
allows	O
for	O
the	O
presence	O
of	O
heteroscedasticity	B-General_Concept
or	O
other	O
effects	O
in	O
the	O
measurement	O
errors	O
.	O
</s>
<s>
Linear	O
errors-in-variables	B-Algorithm
models	I-Algorithm
were	O
studied	O
first	O
,	O
probably	O
because	O
linear	B-Algorithm
models	I-Algorithm
were	O
so	O
widely	O
used	O
and	O
they	O
are	O
easier	O
than	O
non-linear	O
ones	O
.	O
</s>
<s>
Unlike	O
standard	O
least	B-General_Concept
squares	I-General_Concept
regression	O
(	O
OLS	O
)	O
,	O
extending	O
errors	B-Algorithm
in	I-Algorithm
variables	I-Algorithm
regression	O
(	O
EiV	O
)	O
from	O
the	O
simple	O
to	O
the	O
multivariable	O
case	O
is	O
not	O
straightforward	O
.	O
</s>
<s>
The	O
simple	O
linear	O
errors-in-variables	B-Algorithm
model	I-Algorithm
was	O
already	O
presented	O
in	O
the	O
"	O
motivation	O
"	O
section	O
:	O
</s>
<s>
That	O
is	O
,	O
the	O
parameters	O
α	O
,	O
β	O
can	O
be	O
consistently	O
estimated	O
from	O
the	O
data	B-General_Concept
set	I-General_Concept
without	O
any	O
additional	O
information	O
,	O
provided	O
the	O
latent	O
regressor	O
is	O
not	O
Gaussian	O
.	O
</s>
<s>
Deming	B-Algorithm
regression	I-Algorithm
—	O
assumes	O
that	O
the	O
ratio	O
δ	O
=	O
σ²ε/σ²η	O
is	O
known	O
.	O
</s>
<s>
The	O
multivariable	O
model	O
looks	O
exactly	O
like	O
the	O
simple	O
linear	B-Algorithm
model	I-Algorithm
,	O
only	O
this	O
time	O
β	O
,	O
ηt	O
,	O
xt	O
and	O
x*t	O
are	O
k×1	O
vectors	O
.	O
</s>
<s>
Here	O
function	O
g	O
can	O
be	O
either	O
parametric	O
or	O
non-parametric	B-General_Concept
.	O
</s>
<s>
Despite	O
this	O
optimistic	O
result	O
,	O
as	O
of	O
now	O
no	O
methods	O
exist	O
for	O
estimating	O
non-linear	O
errors-in-variables	B-Algorithm
models	I-Algorithm
without	O
any	O
extraneous	O
information	O
.	O
</s>
<s>
With	O
only	O
these	O
two	O
observations	O
it	O
is	O
possible	O
to	O
consistently	O
estimate	O
the	O
density	O
function	O
of	O
x*''	O
using	O
Kotlarski	O
's	O
deconvolution	B-Algorithm
technique	O
.	O
</s>
