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Smooth Discrimination Analysis
 Ann. Statist
, 1998
"... Discriminant analysis for two data sets in IR d with probability densities f and g can be based on the estimation of the set G = fx : f(x) g(x)g. We consider applications where it is appropriate to assume that the region G has a smooth boundary. In particular, this assumption makes sense if di ..."
Abstract

Cited by 154 (3 self)
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Discriminant analysis for two data sets in IR d with probability densities f and g can be based on the estimation of the set G = fx : f(x) g(x)g. We consider applications where it is appropriate to assume that the region G has a smooth boundary. In particular, this assumption makes sense if discriminant analysis is used as a data analytic tool. We discuss optimal rates for estimation of G. 1991 AMS: primary 62G05 , secondary 62G20 Keywords and phrases: discrimination analysis, minimax rates, Bayes risk Short title: Smooth discrimination analysis This research was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373 "Quantifikation und Simulation okonomischer Prozesse", HumboldtUniversitat zu Berlin 1 Introduction Assume that one observes two independent samples X = (X 1 ; : : : ; X n ) and Y = (Y 1 ; : : : ; Ym ) of IR d valued i.i.d. observations with densities f or g, respectively. The densities f and g are unknown. An additional random variabl...
Methods for tracking support boundaries with corners. Unpublished manuscript
, 2001
"... ABSTRACT. In a range of practical problems the boundary of the support of a bivariate distribution is of interest, for example where it describes a limit to efficiency or performance, or where it determines the physical extremities of a spatially distributed population in forestry, marine science, ..."
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Cited by 2 (1 self)
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ABSTRACT. In a range of practical problems the boundary of the support of a bivariate distribution is of interest, for example where it describes a limit to efficiency or performance, or where it determines the physical extremities of a spatially distributed population in forestry, marine science, medicine, meteorology or geology. We suggest a trackingbased method for estimating a support boundary when it is composed of a finite number of smooth curves, meeting together at corners. The smooth parts of the boundary are assumed to have continuously turning tangents and bounded curvature, and the corners are not allowed to be infinitely sharp; that is, the angle between the two tangents should not equal pi. In other respects, however, the boundary may be quite general. In particular it need not be uniquely defined in Cartesian coordinates, its corners my be either concave or convex, and its smooth parts may be neither concave nor convex. Tracking methods are well suited to such generalities, and they also have the advantage of requiring relatively small amounts of computation. It is shown that they achieve optimal convergence rates, in the sense of uniform approximation.
1996, Advances in Applied Probability, 28, 627640. Inference on binary images from binary data
"... Abstract { The problem addressed is to reverse the degradation which occurs when images are digitised: they are blurred, subjected to noise and rounding error, and sampled only at a lattice of points. Inference is considered for the fundamental case of binary scenes, binary data and isotropic blur. ..."
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Abstract { The problem addressed is to reverse the degradation which occurs when images are digitised: they are blurred, subjected to noise and rounding error, and sampled only at a lattice of points. Inference is considered for the fundamental case of binary scenes, binary data and isotropic blur. The inferential process is separable into two stages: rst from the lattice points to a binary image in continuous space and then the reversal of thresholding and blur. Methods are motivated by, and illustrated using, an electron micrograph of an immunogoldlabelled section of tulip virus. 1 1