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SUMMARY:Boundary estimation in the presence of measurement error with unkn
 own variance - Ingrid van Keilegom\, Université catholique de Louvain
DTSTART:20111007T150000Z
DTEND:20111007T160000Z
UID:TALK32519@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:\nBoundary estimation appears naturally in economics in the co
 ntext of productivity analysis. The performance of a firm is measured by t
 he distance between its achieved output level (quantity of goods produced)
  and an optimal production frontier which is the locus of the maximal achi
 evable output given the level of the inputs (labor\, energy\, capital\, et
 c.). Frontier estimation becomes difficult if the outputs are measured wit
 h noise and most approaches rely on restrictive parametric assumptions. Th
 is paper contributes to the direction of nonparametric approaches. A sligh
 tly simplified version of the general problem can be written as Y=X Z\, wh
 ere Y is the observable output\, X is the unobserved variable of interest 
 with support [0\,τ] and density f\, and Z is the noise. Suppose that f(τ
 )>0\, and that Z is independent of X and is log-normally distributed with 
 log Z~N(0\,σ2) for some unknown variance σ 2. The novelty of our approac
 h consists in proposing a method for simultaneous estimation of τ and σ.
  The asymptotic consistency and the rate of convergence of the estimators 
 are established\, and simulations are carried out to verify the performanc
 e of the estimators for small samples. We also describe how the approach c
 ould be extended to the problem of estimating a frontier function. (This i
 s joint work with Alois Kneip and Leopold Simar.)\n\n\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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