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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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