DeepAI AI Chat
Log In Sign Up

Optimal Ridge Detection using Coverage Risk

by   Yen-Chi Chen, et al.
Carnegie Mellon University

We introduce the concept of coverage risk as an error measure for density ridge estimation. The coverage risk generalizes the mean integrated square error to set estimation. We propose two risk estimators for the coverage risk and we show that we can select tuning parameters by minimizing the estimated risk. We study the rate of convergence for coverage risk and prove consistency of the risk estimators. We apply our method to three simulated datasets and to cosmology data. In all the examples, the proposed method successfully recover the underlying density structure.


page 1

page 2

page 3

page 4


Ridge-type Linear Shrinkage Estimation of the Matrix Mean of High-dimensional Normal Distribution

The estimation of the mean matrix of the multivariate normal distributio...

Tuning-free ridge estimators for high-dimensional generalized linear models

Ridge estimators regularize the squared Euclidean lengths of parameters....

Averaging of density kernel estimators

Averaging provides an alternative to bandwidth selection for density ker...

Forest Density Estimation

We study graph estimation and density estimation in high dimensions, usi...

Unbiased estimation and backtesting of risk in the context of heavy tails

While the estimation of risk is an important question in the daily busin...

Filaments of crime: Informing policing via thresholded ridge estimation

Objectives: We introduce a new method for reducing crime in hot spots an...

A Recommendation for Net Undercount Estimation in Iran Population and Dwelling Censuses

Census counts are subject to different types of nonsampling errors. One ...