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CATEGORIES:Statistics
SUMMARY:Boundary estimation in the presence of measurement
error with unknown variance - Ingrid van Keilegom
\, Université catholique de Louvain
DTSTART;TZID=Europe/London:20111007T160000
DTEND;TZID=Europe/London:20111007T170000
UID:TALK32519AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32519
DESCRIPTION:\nBoundary estimation appears naturally in economi
cs in the context of productivity analysis. The pe
rformance of a firm is measured by the distance be
tween its achieved output level (quantity of goods
produced) and an optimal production frontier whic
h is the locus of the maximal achievable output gi
ven the level of the inputs (labor\, energy\, capi
tal\, etc.). Frontier estimation becomes difficult
if the outputs are measured with noise and most a
pproaches rely on restrictive parametric assumptio
ns. This paper contributes to the direction of non
parametric approaches. A slightly simplified versi
on of the general problem can be written as Y=X Z\
, where Y is the observable output\, X is the unob
served variable of interest with support [0\,τ] an
d density f\, and Z is the noise. Suppose that f(τ
)>0\, and that Z is independent of X and is log-no
rmally distributed with log Z~N(0\,σ2) for some un
known variance σ 2. The novelty of our approach co
nsists in proposing a method for simultaneous esti
mation of τ and σ. The asymptotic consistency and
the rate of convergence of the estimators are esta
blished\, and simulations are carried out to verif
y the performance of the estimators for small samp
les. We also describe how the approach could be ex
tended to the problem of estimating a frontier fun
ction. (This is joint work with Alois Kneip and Le
opold Simar.)\n\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Richard Samworth
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