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On nonparametric estimation of intercept and slope distributions in random coefficient regression. (English) Zbl 0867.62021

Summary: An experiment records stimulus and response for a random sample of cases. The relationship between response and stimulus is thought to be linear, the values of the slope and intercept varying by case. From such data, we construct a consistent, asymptotically normal, nonparametric estimator for the joint density of the slope and intercept.
Our methodology incorporates the radial projection-slice theorem for the Radon transform, a technique for locally linear nonparametric regression and a tapered Fourier inversion. Computationally, the new density estimator is more feasible than competing nonparametric estimators, one of which is based on moments and the other on minimum distance considerations.

MSC:

62G07 Density estimation
62J05 Linear regression; mixed models
65C99 Probabilistic methods, stochastic differential equations
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[18] BERKELEY, CALIFORNIA 94720 TORONTO, ONTARIO E-MAIL: beran@stat.berkeley.edu CANADA M5S 3G3 E-MAIL: audrey@utstat.toronto.edu CENTRE FOR MATHEMATICS AND ITS APPLICATIONS AUSTRALIAN NATIONAL UNIVERSITY CANBERRA, ACT 0200 AUSTRALIA E-MAIL: hall@anu.edu.au
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