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SUMMARY:Likelihood based inference for current status data on a grid: a bo
 undary phenomenon and an adaptive inference procedure - Mouli Banerjee\, U
 niversity of Michigan
DTSTART:20120601T150000Z
DTEND:20120601T160000Z
UID:TALK36773@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:In this paper\, we study the nonparametric maximum likelihood 
 estimator (NPMLE)\nfor an event time distribution function at a point in t
 he current status model\nwith observation times supported on a grid of pot
 entially unknown sparsity and\nwith multiple subjects sharing the same obs
 ervation time. This is of interest\nsince observation time ties occur freq
 uently with current status data. The grid\nresolution is specified as c n^
 {-γ} with c > 0 being a scaling constant and γ >\n0 regulating the spars
 ity of the grid relative to the number of subjects (n).\nThe asymptotic be
 havior falls into three cases depending on γ: regular\n‘normal–type
 ’ asymptotics obtain for γ < 1/3\, non-standard cube- root\nasymptotics
  prevail when γ > 1/3 and γ = 1/3 serves as a boundary at which the\ntra
 nsition happens. The limit distribution at the boundary is different from\
 neither of the previous cases and converges weakly to those obtained with 
 γ ∈\n(0\, 1/3) and γ ∈ (1/3\, ∞) as c goes to ∞ and 0\, respecti
 vely. This weak\nconvergence allows us to develop an adaptive procedure to
  construct confidence\nintervals for the value of the event time distribut
 ion at a point of interest\nwithout needing to know or estimate γ\, which
  is of enormous advantage from the\nperspective of inference. A simulation
  study of the adaptive procedure is\npresented.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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