Seminars and Events - Research Colloquia

Special Colloquia, Department of Statistics

Wednesday, February 5, 2003
4:30 PM in REC 307

Dr. Woncheol Jang
Carnegie Mellon University

will speak on

Nonparametric Density Estsimation and Clustering with Application to Cosmology

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 Dümbgen (1998) to construct confidencee sets for the level set {f > δ_c} using the asymptotic distribution of loss function. Specifically, we show the stochastic convergence of the pivot process, B_n(λ_p) = √ n (L_p (λ_p) - Ŝ_p(λ_p)) where L_p(λ_p) and S_p (λ_p) are the loss function and the estimated risk function with the smoothing parameter λ_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.

Acknowledgment

This is joint work with Larry Wasserman, Chris Genovese and Bob Nichol.

References

Beran, R. and Dümbgen. (1998). Modulation of Estimators and Confidence Sets. Ann. Statist., 26, 1826-1856.
Cuevas, A., Febrero, M. and Fraiman, R. (2000). Estimation the number of clusters. The Canadian Journal of Statistics, 28, 367-382.
Jang, W. and Wasserman, L. (2003). Confidencee Sets for Densities and Clusters. In preparation. [4] Stein, C (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist., 9, 1135-1151.
Stein, C (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist., 9, 1135-1151.