Statistical inference on the shape of multivariate curves: mode detection, level set estimation and classification

• Applicant: Professor Dr. Enno Mammen
• Subject Area: Mathematics
• Term: from 2002 to 2006
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5383848

• Final Report Year: 2007

Final Report Abstract

Practical and theoretical advances in density estimation were reached leading to efficient stagewise minimization methods, methods to be applied in time series setting, and for the estimation of the density of random coefficients. The idea of shape isomorphisms was developed to detect the shape of multivariate functions, sets, and data. Level set tree based ideas were applied in mode detection.

Publications

• Package "delt": estimation of multivariate densities with adaptive histograms, R-package
  Klemelä, J.
  
• Package "denpro": visualization of multivariate, functions, sets, and data, R-package
  Klemelä, J.
  
• (2004). Exact constants for pointwise adaptive estimation under the Riesz transform. Probab. Theory Relat. Fields 129, 441-467
  Klemelä, J. and Tsybakov, A. B.
  
• (2004). Visualization of multivariate density estimates with level set trees. J. Comput. Graph. Statist. 13, 599-620
  Klemelä, J.
  
• (2005). Adaptive estimation of the mode of a multivariate density. J. Nonparametr. Statist. 17, 83-105
  Klemelä, J.
  
• (2005). Algorithms for the manipulation of level sets of nonparametric density estimates. Comput. Statist. 20, 349-368
  Klemelä, J.
  
• (2005). Density estimation with locally identically distributed data and with locally stationary data. J. Time Series Analysis
  Klemelä, J.
  
• (2005). Visualization of scales of multivariate density estimates. J. Comput. Graph. Statist.
  Klemelä, J.
  
• (2006). Optimal estimation in additive regression models. Bernoulli. 12, 271-198
  Horowitz, J. and Klemelä, J. and Mammen, E.
  
• (2006). Sharp adaptive estimation of quadratic functionals. Probab. Theory Relat. Fields. 134, 539-564
  Klemelä, J.
  
• (2006). Visualization of multivariate data with tail trees. Information Visualization.
  Klemelä, J.
  
• (2006). Visualization of multivariate density estimates with shape trees. J. Comput. Graph. Statist. 15, 371-397
  Klemelä, J.
  
• (2006). Visualization of the spread of multivariate distributions
  Klemelä, J.
  
• (2007). Density estimation with stagewise optimization of the empirical risk. Machine Learning
  Klemelä, J.
  
• (2007). Reconsidering the random coefficient model
  Hoderlein, S., Klemelä, J., and Mammen, E.