Nonparametric Estimation of Regression Functions in Point Process Models |
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Authors: | Döhler Sebastian Rüschendorf Ludger |
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Institution: | (1) Institute for Mathematical Stochastics, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany |
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Abstract: | We prove that the empirical L
2-risk minimizing estimator over some general type of sieve classes is universally, strongly consistent for the regression
function in a class of point process models of Poissonian type (random sampling processes). The universal consistency result
needs weak assumptions on the underlying distributions and regression functions. It applies in particular to neural net classes
and to radial basis function nets. For the estimation of the intensity functions of a Poisson process a similar technique
yields consistency of the sieved maximum likelihood estimator for some general sieve classes.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | nonparametric estimation regression functions point process models neural nets sieve classes |
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