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DTSTART:20181104T020000
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UID:calendar.1309.field_event_date.0@uwaterloo.ca/statistics-and-actuarial-
science
DTSTAMP:20201203T170030Z
CREATED:20181217T183702Z
DESCRIPTION:ESTIMATION IN PREFERENTIAL ATTACHMENT NETWORKS\n\n\n\nPreferent
ial attachment is widely used to model power-law behavior of degree distri
butions in both directed and undirected networks. Statistical estimates of
the tail exponent of the power-law degree distribution often use the Hill
estimator as one of the key summary statistics\, even though the consiste
ncy of the Hill estimator for network data has not been explored. We deriv
e the asymptotic behavior of the joint degree sequences by embedding the i
n- and out-degrees of a xed node into a pair of switched birth processes w
ith immigration\n and then establish the convergence of the joint tail empi
rical measure. From these steps\, the consistency of the Hill estimators i
s obtained.\n\n\n\nMeanwhile\, one important practical issue of the tail e
stimation problem is how to select a threshold above which observations fo
llow a power-law distribution. A minimum distance selection procedure (MDS
P) has been widely adopted\, especially in the analyses of social networks
. However\, theoretical justications on this selection procedure remain sc
ant. We then study the asymptotic behavior of the optimal threshold and th
e corresponding power-law index given by the MDSP. We also nd that the MDS
P tends to choose too high a threshold level and leads to Hill estimates w
ith large variances and root mean squared errors for simulated data with P
areto-like tails. \n\n\n\nNote: This is based on joint works with S.I. Res
nick (Cornell University\, US)\, H. Drees (University of Hamburg\, Germany
) and A. Janen (KTH Royal Institute of Technology\, Sweden).
DTSTART;TZID=America/Toronto:20190111T160000
DTEND;TZID=America/Toronto:20190111T160000
LAST-MODIFIED:20181219T141921Z
LOCATION:M3 - Mathematics 3\n \n\n Room: 3127 \n
\n\n \n\n 200 University Avenue West \n
Waterloo\, ON\n
N2L 3G1\n \nCanada
SUMMARY:Department seminar by Tiandong Wang\, Cornell University
URL;TYPE=URI:https://uwaterloo.ca/statistics-and-actuarial-science/events/d
epartment-seminar-tiandong-wang-cornell-university
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