<s>
In	O
statistics	O
,	O
the	O
Hannan	B-General_Concept
–	I-General_Concept
Quinn	I-General_Concept
information	I-General_Concept
criterion	I-General_Concept
(	O
HQC	B-General_Concept
)	O
is	O
a	O
criterion	O
for	O
model	O
selection	O
.	O
</s>
<s>
It	O
is	O
an	O
alternative	O
to	O
Akaike	O
information	O
criterion	O
(	O
AIC	O
)	O
and	O
Bayesian	B-General_Concept
information	I-General_Concept
criterion	I-General_Concept
(	O
BIC	B-General_Concept
)	O
.	O
</s>
<s>
Burnham	O
&	O
Anderson	O
(	O
2002	O
,	O
p.287	O
)	O
say	O
that	O
HQC	B-General_Concept
,	O
"	O
while	O
often	O
cited	O
,	O
seems	O
to	O
have	O
seen	O
little	O
use	O
in	O
practice	O
"	O
.	O
</s>
<s>
They	O
also	O
note	O
that	O
HQC	B-General_Concept
,	O
like	O
BIC	B-General_Concept
,	O
but	O
unlike	O
AIC	O
,	O
is	O
not	O
an	O
estimator	O
of	O
Kullback	O
–	O
Leibler	O
divergence	O
.	O
</s>
<s>
Claeskens	O
&	O
Hjort	O
(	O
2008	O
,	O
ch.4	O
)	O
note	O
that	O
HQC	B-General_Concept
,	O
like	O
BIC	B-General_Concept
,	O
but	O
unlike	O
AIC	O
,	O
is	O
not	O
asymptotically	O
efficient	O
;	O
however	O
,	O
it	O
misses	O
the	O
optimal	O
estimation	O
rate	O
by	O
a	O
very	O
small	O
factor	O
.	O
</s>
<s>
They	O
further	O
point	O
out	O
that	O
whatever	O
method	O
is	O
being	O
used	O
for	O
fine-tuning	O
the	O
criterion	O
will	O
be	O
more	O
important	O
in	O
practice	O
than	O
the	O
term	O
,	O
since	O
this	O
latter	O
number	O
is	O
small	O
even	O
for	O
very	O
large	O
;	O
however	O
,	O
the	O
term	O
ensures	O
that	O
,	O
unlike	O
AIC	O
,	O
HQC	B-General_Concept
is	O
strongly	O
consistent	O
.	O
</s>
<s>
It	O
follows	O
from	O
the	O
law	O
of	O
the	O
iterated	O
logarithm	O
that	O
any	O
strongly	O
consistent	O
method	O
must	O
miss	O
efficiency	O
by	O
at	O
least	O
a	O
factor	O
,	O
so	O
in	O
this	O
sense	O
HQC	B-General_Concept
is	O
asymptotically	O
very	O
well-behaved	O
.	O
</s>
<s>
Van	O
der	O
Pas	O
and	O
Grünwald	O
prove	O
that	O
model	O
selection	O
based	O
on	O
a	O
modified	O
Bayesian	O
estimator	O
,	O
the	O
so-called	O
switch	O
distribution	O
,	O
in	O
many	O
cases	O
behaves	O
asymptotically	O
like	O
HQC	B-General_Concept
,	O
while	O
retaining	O
the	O
advantages	O
of	O
Bayesian	O
methods	O
such	O
as	O
the	O
use	O
of	O
priors	O
etc	O
.	O
</s>
