Jussi Klemelä

Jussi Klemelä
University of Oulu
Department of Mathematical Sciences
P.O. Box 3000
90014 University of Oulu, Finland

Email: jussi.klemela at oulu.fi
Phone: +358-8-553 1754
Fax: +358-8-553 1730
Office: Pentti Kaiteran katu 1, M207

Nonparametric function estimation

Teaching

• Ekonometrian tilastolliset perusteet 805339A, Kevät 2010
• Rahoituksen tilastotiede/Statistical finance
• Nonparametric function estimation with applications in finance

Book

The homepage of the book contains preview, blog, software, the figures, and advice to their reproduction.

Preprints

• J. Klemelä and E. Mammen. Empirical risk minimization in inverse problems: Extended technical version, 2009. (PDF)


• S. Hoderlein, J. Klemelä, and E. Mammen. Analyzing the random coefficient model nonparametrically, 2008. (PDF)


• J. Klemelä Density estimation with stagewise optimization of the empirical risk, 2005. (compressed PostScript, PDF)


• J. Klemelä. Density estimation with locally identically distributed data and with locally stationary data, 2005. (PostScript, PDF)


• J. Klemelä. Complexity penalized support estimation, 2002. (gzipped PostScript, PDF, Abstract and software)


• J. Klemelä. Multivariate histograms with data-dependent partitions, 2001. (PDF)


• J. Klemelä. Optimal recovery and statistical estimation in Lp Sobolev classes, 2003. (PostScript, PDF, Homepage of the article)


• J. Horowitz, J. Klemelä and E. Mammen. Optimal estimation in additive regression. 2002.


• J. Klemelä and A. B. Tsybakov. Exact constants for pointwise adaptive estimation under the Riesz transform, 2001. (PostScript, PDF)


• J. Klemelä. Adaptive estimation of the location of the mode of a multivariate density, 2000. (gzipped PostScript)


• J. Klemelä. Sharp adaptive estimation of quadratic functionals. Prépublication 529, Laboratoire de Probabilités et Modèles Aléatoires, Universités de Paris 6 et Paris 7, 1999. (PostScript, PDF, Abstract and software)


• J. Klemelä and A. B. Tsybakov. Sharp adaptive estimation of linear functionals. Prépublication 540, Laboratoire de Probabilités et Modèles Aléatoires, Universités de Paris 6 et Paris 7, 1999. (PostScript, PDF)

• J. Klemelä. Analysis of the shapes of unimodal densities with nonparametric density estimation, 2008. (PDF)


• J. Klemelä. Level set trees and the analysis of shapes, 2008. (PDF)


• J. Klemelä. Prototypes of visualization tools, 2006. (PDF)


• J. Klemelä. Visualization of the spread of multivariate distributions, 2005. (gzipped PostScript, PDF)


• J. Klemelä. Visualization of scales of multivariate density estimates, 2005. (PDF)


• J. Klemelä. Visualization of multivariate data with tail trees, 2005. (PDF)


• J. Klemelä. Visualization of multivariate density estimates with shape trees, 2004. (gzipped PostScript , PDF)


• J Klemelä. Algorithms for manipulation of level sets of nonparametric density estimates, 2003. (gzipped PostScript, PDF, Homepage of the article)


• J. Klemelä. Visualization of multivariate density estimates with level set trees, 2000. (gzipped PostScript, PDF, Homepage of the article , Software )

• J. Klemelä. Lower bounds for the asymptotic minimax risk with spherical data, 2000. (PostScript)


• J. Klemelä. Asymptotic minimax risk in the uniform norm for the white noise model on the sphere. Discussion Paper 21, Sonderforschungbereich 373, Humboldt Universität, Berlin, 1998. (PostScript)


• J. Klemelä. Estimation of densities and derivatives of densities at a point with spherical data. Technical report, 1997. Partly published in Journal of Multivariate Analysis, 73:18-40,2000. (PostScript)


• J. Klemelä. Integrated risk of the kernel estimator with spherical data. Technical report, 1997. Partly published in Journal of Multivariate Analysis, 73:18-40,2000. (PostScript)


• J. Klemelä. Estimation of densities and functionals of densities with spherical data. A 16, Rolf Nevanlinna Institute, 1997

Software

• R-package "denpro" for the visualization of multivariate density estimates.


• R-package "delt" for the estimation of multivariate densities with adaptive histograms.


• R-package "finatool" for portfolio selection and pricing and hedging of options. The package will be written during spring 2009.

Selected publications

• J. Klemelä and E. Mammen. (2010). Empirical risk minimization in inverse problems Ann. Statist. 38(1): 482-511.


• J. Klemelä. (2007). Visualization of multivariate data with tail trees. Information Visualization 6: 109-122.


• J. Klemelä. (2006). Sharp adaptive estimation of quadratic functionals. Probab. Theory Relat. Fields. 134(4): 539-564.


• J. Klemelä. (2004). Visualization of multivariate density estimates with level set trees. J. Comput. Graph. Statist. 13(3): 599-620.


• J. Klemelä and A. B. Tsybakov. (2001). Sharp adaptive estimation of linear functionals. Ann. Statist. 29: 1567-1600.

Animations

• Animations on density estimation
  • Growing of a level set tree tree
  • Growing of a shape tree
  • Growing of a tail tree
  • Slices of a function
  • CART visualization vs. level set tree visualization
• Animations on statistical finance
  • Scatter matrices
  • Scatter matrices; copula transformed data
  • Scatter matrices; original data
  • Hedging
  • Hedging with Gaussian asset prices
  • Hedging with Student asset prices
  • Hedging of an ATM option with Gaussian and Student asset prices
  • Profit distributions
  • Profit distributions of call options
  • Profit distributions of strangles
  • Profit distributions of condors
    • Movie I
    • Movie II

Talks

• Analysis of dependency with density estimation (PDF)
• Level set trees and the analysis of shapes (PDF)
• Likelihood subsetting of financial data (PDF)
• Empirical risk minimization in inverse problems (PDF)
• Density estimation with stagewise optimization of the empirical risk (PDF)
• Visualization of multivariate functions, sets, and data (PDF)
• Visualization of multivariate density estimates with shape trees (PDF)
• Visualization of multivariate density estimates (PDF)

Lectures on nonparametric function estimation

In nonparametric function estimation one approximates and interpolates functions when only noisy data is available. Functions to be estimated include probability density functions, regression functions, spectral density functions, and intensity functions. The lectures will concentrate on the estimation and visualization of multivariate density functions, but the techniques apply also to other kinds of functions. The estimation techniques include the use of anisotropic kernel estimators, minimization estimators, multivariate adaptive histograms, wavelet estimators, best basis selection, and stagewise minimization.

• Lecture I, 1.10.2007 (PDF)
• Lecture II, 15.10.2007 (PDF)
• Lecture III, 29.10.2007 (PDF)
• Lecture IV, 12.11.2007 (PDF)
• Lecture V, 26.11.2007 (PDF)
• Lecture VI, 10.12.2007 (PDF)