Joint work with Larry Wasserman, Chris Genovese and Bob Nichol.
Abstract
We present a clustering method based on nonparametric density
estimation. We use Kernel smoothing and orthogonal series estimators
to estimate the density f and then we extract the connected components
of the level set using a modified Cuevas et al (2000) algorithm. We
extend an idea due to Stein (1981) and Beran and Dumbgen (1998) to
construct confidence sets for the level set {f > delta_c} using the
asymptotic distribution of loss function. Specifically, we show the
stochastic convergence of the pivot process, B_n(lambda_p) =
sqrt(n) * (L_p(lambda_p)  S_hat_p(lambda_p)) where L_p(lambda_p) and
S_p(lambda_p) are the loss function and the estimated risk function
with the smoothing parameter lambda_p. Inverting the pivot provides a
confidence set for the coefficient of the orthogonal series estimator
and furthermore one can construct a confidence set for functionals of
f . We consider applications in astronomy and other fields.
References

Charles Rosenberg Last modified: Thu Jan 23 11:54:49 EST 2003