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CATEGORIES:Statistics
SUMMARY:Likelihood based inference for current status data
  on a grid: a boundary phenomenon and an adaptive 
 inference procedure - Mouli Banerjee\, University 
 of Michigan
DTSTART;TZID=Europe/London:20120601T160000
DTEND;TZID=Europe/London:20120601T170000
UID:TALK36773AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36773
DESCRIPTION:In this paper\, we study the nonparametric maximum
  likelihood estimator (NPMLE)\nfor an event time d
 istribution function at a point in the current sta
 tus model\nwith observation times supported on a g
 rid of potentially unknown sparsity and\nwith mult
 iple subjects sharing the same observation time. T
 his is of interest\nsince observation time ties oc
 cur frequently with current status data. The grid\
 nresolution is specified as c n^{-γ} with c > 0 be
 ing a scaling constant and γ >\n0 regulating the s
 parsity of the grid relative to the number of subj
 ects (n).\nThe asymptotic behavior falls into thre
 e cases depending on γ: regular\n‘normal–type’ asy
 mptotics obtain for γ < 1/3\, non-standard cube- r
 oot\nasymptotics prevail when γ > 1/3 and γ = 1/3 
 serves as a boundary at which the\ntransition happ
 ens. The limit distribution at the boundary is dif
 ferent from\neither of the previous cases and conv
 erges 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\nint
 ervals for the value of the event time distributio
 n at a point of interest\nwithout needing to know 
 or estimate γ\, which is of enormous advantage fro
 m the\nperspective of inference. A simulation stud
 y of the adaptive procedure is\npresented.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
 B
CONTACT:Richard Samworth
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