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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, November 23, 1999}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Erik van Zwet}
\centerline{\sl visiting UC Berkeley}
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\centerline{\bf Statistics of a windowed linesegment process}
\centerline{\bf }
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We want to estimate the length distribution of fractures in a rock surface
on the basis of a geological map. We do not fully observe the fractures
because parts of the rock surface are covered by vegetation, soil and
water. This covered region is very irregular. In fact, it is not convex.
This means that we might observe several fragments of a single fracture. It
is quite impossible to decide from the map if two nearby fragments belong
to the same fracture. We therefore simplify by pretending that, instead of
the fractures, the observed fragments are independent. For this simpler
model we find the nonparametric maximum likelihood estimator of the length
distribution. We then apply this estimator to the original problem and show
its consistency.

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